In this particular stanza Lord Śrī Kṛṣṇa, the Personality of Godhead, is distinguished from other incarnations. He is counted amongst the avatāras (incarnations) because out of His causeless mercy the Lord descends from His transcendental abode. Avatāra means "one who descends." All the incarnations of the Lord, including the Lord Himself, descend on the different planets of the material world as also in different species of life to fulfill particular missions. Sometimes He comes Himself, and sometimes His different plenary portions or parts of the plenary portions, or His differentiated portions directly or indirectly empowered by Him, descend on this material world to execute certain specific functions. Originally the Lord is full of all opulences, all prowess, all fame, all beauty, all knowledge and all renunciation. When they are partly manifested through the plenary portions or parts of the plenary portions, it should be noted that certain manifestations of His different powers are required for those particular functions. When in the room small electric bulbs are displayed, it does not mean that the electric powerhouse is limited by the small bulbs. The same powerhouse can supply power to operate large-scale industrial dynamos with greater volts. Similarly, the incarnations of the Lord display limited powers because so much power is needed at that particular time.
For example, Lord Paraśurāma and Lord Nṛsiṁha displayed unusual opulence by killing the disobedient kṣatriyas twenty-one times and killing the greatly powerful atheist Hiraṇyakaśipu. Hiraṇyakaśipu was so powerful that even the demigods in other planets would tremble simply by the unfavorable raising of his eyebrow. The demigods in the higher level of material existence many, many times excel the most well-to-do human beings, in duration of life, beauty, wealth, paraphernalia, and in all other respects. Still they were afraid of Hiraṇyakaśipu. Thus we can simply imagine how powerful Hiraṇyakaśipu was in this material world. But even Hiraṇyakaśipu was cut into small pieces by the nails of Lord Nṛsiṁha. This means that anyone materially powerful cannot stand the strength of the Lord's nails.
(Srimad Bhagavatam------1:3:28------purport).

Paraśurāma, or Reṇukāsuta: He is the son of Maharṣi Jamadagni and Śrīmatī Reṇukā. Thus he is also known as Reṇukāsuta. He is one of the powerful incarnations of God, and he killed the kṣatriya community as a whole twenty-one times. With the blood of the kṣatriyas he pleased the souls of his forefathers. Later on he underwent severe penances at the Mahendra Parvata. After taking the whole earth from the kṣatriyas, he gave it in charity to Kaśyapa Muni. Paraśurāma instructed the Dhanur-veda, or the science of fighting, to Droṇācārya because he happened to be a brāhmaṇa. He was present during the coronation of Mahārāja Yudhiṣṭhira, and he celebrated the function along with other great ṛṣis.
Paraśurāma is so old that he met both Rāma and Kṛṣṇa at different times. He fought with Rāma, but he accepted Kṛṣṇa as the Supreme Personality of Godhead. He also praised Arjuna when he saw him with Kṛṣṇa. When Bhīṣma refused to marry Ambā, who wanted him to become her husband, Ambā met Paraśurāma, and by her request only, he asked Bhīṣmadeva to accept her as his wife. Bhīṣma refused to obey his order, although he was one of the spiritual masters of Bhīṣmadeva. Paraśurāma fought with Bhīṣmadeva when Bhīṣma neglected his warning. Both of them fought very severely, and at last Paraśurāma was pleased with Bhīṣma and gave him the benediction of becoming the greatest fighter in the world.
(Srimad Bhagavatam------1:9:6-7------purport).

The kṣatriyas, or the ruling administrators of any part of the universe, either on this planet or on other planets, are factually the representatives of the Almighty Personality of Godhead, and they are meant to lead the subjects towards the path of God realization. Every state and its administrators, regardless of the nature of the administration—monarchy or democracy, oligarchy or dictatorship or autocracy—have the prime responsibility to lead the citizens toward God realization. This is essential for all human beings, and it is the duty of the father, spiritual master, and ultimately the state to take up the responsibility of leading the citizens towards this end. The whole creation of material existence is made for this purpose, just to give a chance to the fallen souls who rebelled against the will of the Supreme Father and thus became conditioned by material nature. The force of material nature gradually leads one to a hellish condition of perpetual pains and miseries. Those going against the prescribed rules and regulations of conditional life are called brahmojjhita-pathas, or persons going against the path of the Absolute Truth, and they are liable to be punished. Lord Paraśurāma, the incarnation of the Personality of Godhead, appeared in such a state of worldly affairs and killed all the miscreant kings twenty-one times. Many kṣatriya kings fled from India to other parts of the world at that time, and according to the authority of the Mahābhārata, the kings of Egypt originally migrated from India because of Paraśurāma's program of chastisement. The kings or administrators are similarly chastised in all circumstances whenever they become godless and plan a godless civilization. That is the order of the Almighty.
(Srimad Bhagavatam------2:7:22------purport).

The Supreme indestructible Lord is ascertained through the performance of ritualistic sacrifices and is therefore known as Yajñeśvara. In His incarnation as Lord Boar, He raised the planet earth from the water at the bottom of the universe and kept it on His pointed tusks. May that Lord protect me from rogues on the street. May Paraśurāma protect me on the tops of mountains, and may the elder brother of Bharata, Lord Rāmacandra, along with His brother Lakṣmaṇa, protect me in foreign countries.
There are three Rāmas. One Rāma is Paraśurāma (Jāmadāgnya), another Rāma is Lord Rāmacandra, and a third Rāma is Lord Balarāma. In this verse the words rāmo'dri-kūṭeṣv atha indicate Lord Paraśurāma. The brother of Bharata Mahārāja and Lakṣmaṇa is Lord Rāmacandra.
(Srimad Bhagavatam------6:8:15------translation and purport).

The son of Aśmaka was known as Bālika. He was protected from the curse of Paraśurāma because of being surrounded by many women, and therefore he is also known as Nārīkavaca. When the entire world was devoid of kṣatriyas, he became the original father of more kṣatriyas. He is therefore sometimes called Mūlaka. From Bālika, Daśaratha was born, from Daśaratha came Aiḍaviḍi, and from Aiḍaviḍi came Viśvasaha. The son of Viśvasaha was Mahārāja Khaṭvāṅga. Mahārāja Khaṭvāṅga joined the demigods in fighting the demons and was victorious, and the demigods therefore wanted to give him a benediction. But when the King inquired how long he would live and understood that his life would last only a few seconds more, he immediately left the heavenly planets and returned to his own abode by airplane. He could understand that everything in this material world is insignificant, and thus he fully engaged in worshiping the Supreme Personality of Godhead, Hari.
(Srimad Bhagavatam------9:9------summary).

From the womb of Urvaśī came six sons, named Āyu, Śrutāyu, Satyāyu, Raya, Jaya and Vijaya. The son of Śrutāyu was Vasumān, the son of Satyāyu was Śrutañjaya, the son of Raya was Eka, the son of Jaya was Amita, and the son of Vijaya was Bhīma. Bhīma's son was named Kāñcana, the son of Kāñcana was Hotraka, and the son of Hotraka was Jahnu, who was celebrated for having drunk all the water of the Ganges in one sip. The descendants of Jahnu, one after another, were Puru, Balāka, Ajaka and Kuśa. The sons of Kuśa were Kuśāmbu, Tanaya, Vasu and Kuśanābha. From Kuśāmbu came Gādhi, who had a daughter named Satyavatī. Satyavatī married Ṛcīka Muni after the muni contributed a substantial dowry, and from the womb of Satyavatī by Ṛcīka Muni, Jamadagni was born. The son of Jamadagni was Rāma, or Paraśurāma. When a king named Kārtavīryārjuna stole Jamadagni's desire cow, Paraśurāma, who is ascertained by learned experts to be a saktyāveśa incarnation of the Supreme Personality of Godhead, killed Kārtavīryārjuna. Later, he annihilated the kṣatriya dynasty twenty-one times. After Paraśurāma killed Kārtavīryārjuna, Jamadagni told him that killing a king is sinful and that as a brāhmaṇa he should have tolerated the offense. Therefore Jamadagni advisedParaśurāma to atone for his sin by traveling to various holy places.
(Srimad Bhagavatam------9:15------summary).

When the royal dynasty, being excessively proud because of the material modes of passion and ignorance, became irreligious and ceased to care for the laws enacted by the brāhmaṇas, Paraśurāma killed them. Although their offense was not very severe, he killed them to lessen the burden of the world.
The kṣatriyas, or the ruling class, must govern the world in accordance with the rules and regulations enacted by great brāhmaṇas and saintly persons. As soon as the ruling class becomes irresponsible in regard to the religious principles, it becomes a burden on the earth. As stated here, rajas-tamo-vṛtaṁ, bhāram abrahmaṇyam: when the ruling class is influenced by the lower modes of nature, namely ignorance and passion, it becomes a burden to the world and must then be annihilated by superior power. We actually see from modern history that monarchies have been abolished by various revolutions, but unfortunately the monarchies have been abolished to establish the supremacy of third-class and fourth-class men. Although monarchies overpowered by the modes of passion and ignorance have been abolished in the world, the inhabitants of the world are still unhappy, for although the qualities of the former monarchs were degraded by taints of ignorance, these monarchs have been replaced by men of the mercantile and worker classes whose qualities are even more degraded. When the government is actually guided by brāhmaṇas, or God conscious men, then there can be real happiness for the people. Therefore in previous times, when the ruling class was degraded to the modes of passion and ignorance, the brāhmaṇas, headed by such a kṣatriya-spirited brāhmaṇa as Paraśurāma, killed them twenty-one consecutive times.
(Srimad Bhagavatam------9:15:15------translation and purport).

The Brahma-saṁhitā informs us that the spiritual world, and especially the planet Goloka Vṛndāvana, where Kṛṣṇa lives, is full of surabhi cows (surabhīr abhipālayantam (Bs. 5.29)). The surabhi cow is also called kāmadhenu. Although Jamadagni possessed only one kāmadhenu, he was able to get from it everything desirable. Thus he was able to receive the King, along with the King's great number of followers, ministers, soldiers, animals and palanquin carriers. When we speak of a king, we understand that he is accompanied by many followers. Jamadagni was able to receive all the King's followers properly and feed them sumptuously with food prepared in ghee. The King was astonished at how opulent Jamadagni was because of possessing only one cow, and therefore he became envious of the great sage. This was the beginning of his offense. Paraśurāma, the incarnation of the Supreme Personality of Godhead, killed Kārtavīryārjuna because Kārtavīryārjuna was too proud. One may possess unusual opulence in this material world, but if one becomes puffed up and acts whimsically he will be punished by the Supreme Personality of Godhead. This is the lesson to learn from this history, in which Paraśurāma became angry at Kārtavīryārjuna and killed him and rid the entire world of kṣatriyas twenty-one times.
(Srimad Bhagavatam------9:15:24------purport).

When Jamadagni was killed by the sons of Kārtavīryārjuna, as described in this chapter, Paraśurāma rid the entire world of kṣatriyas twenty-one times. This chapter also describes the descendants of Viśvāmitra.
When Jamadagni's wife, Reṇukā, went to bring water from the Ganges and saw the King of the Gandharvas enjoying the company of Apsarās, she was captivated, and she slightly desired to associate with him. Because of this sinful desire, she was punished by her husband. Paraśurāma killed his mother and brothers, but later, by dint of the austerities of Jamadagni, they were revived. The sons of Kārtavīryārjuna, however, remembering the death of their father, wanted to take revenge against Lord Paraśurāma, and therefore when Paraśurāma was absent from the āśrama, they killed Jamadagni, who was meditating on the Supreme Personality of Godhead. When Paraśurāma returned to the āśrama and saw his father killed, he was very sorry, and after asking his brothers to take care of the dead body, he went out with determination to kill all the kṣatriyas on the surface of the world. Taking up his axe, he went to Māhiṣmatī-pura, the capital of Kārtavīryārjuna, and killed all of Kārtavīryārjuna's sons, whose blood became a great river. Paraśurāma, however, was not satisfied with killing only the sons of Kārtavīryārjuna; later, when the kṣatriyas became disturbing, he killed them twenty-one times, so that there were no kṣatriyas on the surface of the earth. Thereafter, Paraśurāmajoined the head of his father to the dead body and performed various sacrifices to please the Supreme Lord. Thus Jamadagni got life again in his body, and later he was promoted to the higher planetary system known as Saptarṣi-maṇḍala. Paraśurāma, the son of Jamadagni, still lives in Mahendra-parvata. In the next manvantara, he will become a preacher of Vedic knowledge.
(Srimad Bhagavatam------9:16------summary).

With the blood of the bodies of these sons, Lord Paraśurāma created a ghastly river, which brought great fear to the kings who had no respect for brahminical culture. Because the kṣatriyas, the men of power in government, were performing sinful activities, Lord Paraśurāma, on the plea of retaliating for the murder of his father, rid all the kṣatriyas from the face of the earth twenty-one times. Indeed, in the place known as Samanta-pañcaka he created nine lakes filled with their blood.
Paraśurāma is the Supreme Personality of Godhead, and his eternal mission is paritrāṇāya sādhūnāṁ vināśāya ca duṣkṛtām (B.G.4:8)—to protect the devotees and annihilate the miscreants. To kill all the sinful men is one among the tasks of the incarnation of Godhead. Lord Paraśurāma killed all the kṣatriyas twenty-one times consecutively because they were disobedient to the brahminical culture. That the kṣatriyas had killed his father was only a plea; the real fact is that because the kṣatriyas, the ruling class, had become polluted, their position was inauspicious. Brahminical culture is enjoined in the śāstra, especially in Bhagavad-gītā (cātur-varṇyaṁ mayā sṛṣṭaṁ guṇa-karma-vibhāgaśaḥ (B.G.4:13). According to the laws of nature, whether at the time of Paraśurāma or at the present, if the government becomes irresponsible and sinful, not caring for brahminical culture, there will certainly be an incarnation of God like Paraśurāma to create a devastation by fire, famine, pestilence or some other calamity. Whenever the government disrespects the supremacy of the Personality of Godhead and fails to protect the institution of varṇāśrama-dharma, it will certainly have to face such catastrophes as formerly brought about by Lord Paraśurāma.
(Srimad Bhagavatam------9:16:18-19------translation and purport).

These are some of the reasons why Balarāma is known as Saṅkarṣaṇa, Balarāma or sometimes Rāma. In the mahā-mantra—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—people sometimes object when Rāma is accepted as Balarāma. But although devotees of Lord Rāma may object, they should know that there is no difference between Balarāma and Lord Rāma. Here Śrīmad-Bhāgavatam clearly states that Balarāma is also known as Rāma (rāmeti). Therefore, it is not artificial for us to speak of Lord Balarāma as Lord Rāma. Jayadeva Gosvāmī also speaks of three Rāmas: Paraśurāma, Raghupati Rāma and Balarāma. All of them are Rāmas.
(Srimad Bhagavatam------10:2:13------purport).