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.
(Srimad Bhagavatam----1:3:38----purport).

The Personality of Godhead Lord Viṣṇu descends by His will to the material planets in His innumerable incarnations for particular purposes, and again He goes back to His own abode. When He descends He is called an avatāra because avatāra means "one who descends." Neither the Lord Himself nor His specific devotees who come to this earth are ordinary living entities like us.
(Srimad Bhagavatam----3:13:47----purport).

The Lord descends from His abode to this world, and therefore He is called avatāra, which means "one who descends." Sometimes avatāra is understood to refer to an incarnation who assumes a material form of flesh and bone, but actually avatāra refers to one who descends from higher regions. The Lord's abode is situated far above this material sky, and He descends from that higher position; thus He is called avatāra.
(Srimad Bhagavatam----3:19:31----purport).

This path of acceptance is called avaroha-panthā The word avaroha is related to the word avatāra, which means"that which descends." The materialist wants to understand everything by the āroha-panthā—by argument and reason—but transcendental matters cannot be understood in this way. Rather, one must follow the avaroha-panthā, the process of descending knowledge. Therefore one must accept the paramparā system. And the best paramparā is that which extends from Kṛṣṇa (evaṁ paramparā-prāptam (B.G.4:2). What Kṛṣṇa says, we should accept (imaṁ rājarṣayo viduḥ). This is called the avaroha-panthā.
(Srimad Bhagavatam----10:13:57----purport).

Lord Caitanya continued to explain to Sanātana Gosvāmī that the expansions of Lord Kṛṣṇa who come to the material creation are called avatāras, or incarnations. The word avatāra means "One who descends," and in this case the word specifically refers to one who descends from the spiritual sky. In the spiritual sky there are innumerable Vaikuṇṭha planets, and from these planets the expansions of the Supreme Personality of Godhead come into this universe.
(Teachings of Lord Caitanya).