Generally, a man is born as an ordinary being, and by the purificatory processes he is born for the second time. When he sees a new light and seeks direction for spiritual progress, he approaches a spiritual master for instruction in the Vedas. The spiritual master accepts only the sincere inquirer as his disciple and gives him the sacred thread. In this way a man becomestwice-born, or a dvija. After qualifying as a dvija one may study the Vedas, and after becoming well versed in the Vedas one becomes a vipra. A vipra, or a qualified brāhmaṇa, thus realizes the Absolute and makes further progress in spiritual life until he reaches the Vaiṣṇava stage. The Vaiṣṇava stage is the postgraduate status of a brāhmaṇa. A progressive brāhmaṇa must necessarily become a Vaiṣṇava, for a Vaiṣṇava is a self-realized, learned brāhmaṇa.
(Srimad Bhagavatam---------1:2:2--------purport).

Even those who are born by a brāhmaṇa father are, in the present age, no better than the śūdras or the women. The twice-born men, namely the brāhmaṇas, kṣatriyas and vaiśyas, are expected to undergo a cultural purificatory process known as saṁskāras, but because of the bad influence of the present age the so-called members of the brāhmaṇa and other high-order families are no longer highly cultured. They are called the dvija-bandhus, or the friends and family members of the twice-born. But these dvija-bandhus are classified amongst the śūdras and the women. Śrīla Vyāsadeva divided the Vedas into various branches and subbranches for the sake of the less intelligent classes like the dvija-bandhus, śūdras and women.
(Srimad Bhagavatam---------1:3:21--------purport).

Because Śrīmad-Bhāgavatam is the special contribution of Śrīla Vyāsadeva, there are so many inquiries by the learned Śaunaka Muni. It was known to them that Śrīla Vyāsadeva had already explained the text of the Vedas in various ways up to the Mahābhārata for the understanding of less intelligent women, śūdras and fallen members of the family oftwice-born men. Śrīmad-Bhāgavatam is transcendental to all of them because it has nothing to do with anything mundane. So the inquiries are very intelligent and relevant.
(Srimad Bhagavatam---------1:4:3--------purport).

The friends of the twice-born families are those who are born in the families of brāhmaṇas, kṣatriyas and vaiśyas, or the spiritually cultured families, but who themselves are not equal to their forefathers. Such descendants are not recognized as such, for want of purificatory achievements. The purificatory activities begin even before the birth of a child, and the seed-giving reformatory process is called Garbhādhāna-saṁskāra. One who has not undergone such Garbhādhāna-saṁskāra, or spiritual family planning, is not accepted as being of an actual twice-born family. The Garbhādhāna-saṁskāra is followed by other purificatory processes, out of which the sacred thread ceremony is one. This is performed at the time of spiritual initiation. After this particular saṁskāra, one is rightly called twice-born. One birth is calculated during the seed-giving saṁskāra, and the second birth is calculated at the time of spiritual initiation. One who has been able to undergo such important saṁskāras can be called a bona fide twice-born.
(Srimad Bhagavatam---------1:4:25--------purport).

If the father and the mother do not undertake the process of spiritual family planning and simply beget children out of passion only, their children are called dvija-bandhus. These dvija-bandhus are certainly not as intelligent as the children of the regular twice-born families. The dvija-bandhus are classified with the śūdras and the woman class, who are by nature less intelligent. The śūdras and the woman class do not have to undergo any saṁskāra save and except the ceremony of marriage.
(Srimad Bhagavatam---------1:4:25--------purport).

Lord Śrī Kṛṣṇa was invited by Mahārāja Yudhiṣṭhira to look into the supervision of the performances of yajña, and the Lord, to abide by the orders of His elderly cousin, caused the performance of yajñas by learned twice-born brāhmaṇas. Simply taking birth in the family of a brāhmaṇa does not make one qualified to perform yajñas. One must betwice-born by proper training and initiation from the bona fide ācārya. The once-born scions of brāhmaṇa families are equal with the once-born śūdras, and such brahma-bandhus, or unqualified once-born scions, must be rejected for any purpose of religious or Vedic function. Lord Śrī Kṛṣṇa was entrusted to look after this arrangement, and perfect as He is, He caused the yajñas to be performed by the bona fide twice-born brāhmaṇas for successful execution.
(Srimad Bhagavatam---------1:12:35--------purport).

The brāhmaṇas, kṣatriyas and vaiśyas are called twice-born because for these higher classes of men there is one birth by parental conjugation and there is another birth of cultural rejuvenation by spiritual initiation from the bona fide ācārya, or spiritual master. So a kṣatriya is also twice-born like a brāhmaṇa, and his duty is to give protection to the helpless. The kṣatriya king is considered to be the representative of God to give protection to the helpless and chastise the miscreants.
(Srimad Bhagavatam---------1:17:5--------purport).

Because of the lack of training or culture in the upper section of the social orders, they are no more to be designated as the dvija janas, or the twice-born. The significance of being twice-born has been explained in many places in these great literatures, and again one is reminded herewith that birth, executed by the sex life of the father and the mother, is called animal birth. But such animal birth and progress of life on the animal principles of eating, sleeping, fearing and mating (without any scientific culture of spiritual life) is called the śūdra life, or, to be more explicit, the uncultured life of the lower class of men.
(Srimad Bhagavatam---------2:7:38--------purport).

The Lord's pastimes for the protection of the twice-born civilized men, the cows and the demigods are all transcendental. A human being is inclined to hear good narrations and stories, and therefore there are so many books, magazines and newspapers on the market to satisfy the interests of the developed soul. But the pleasure in such literature, after it is read once, becomes stale, and people do not take any interest in reading such literature repeatedly.
(Srimad Bhagavatam---------3:5:7--------purport).

It is also affirmed herein that the brāhmaṇas are the best of the twice-born. Brāhmaṇas, kṣatriyas and vaiśyas are all twice-born, but the brāhmaṇas are the best. When there is a fight between two persons, each of them protects the upper part of his body—the head, the arms and the belly. Similarly, for the actual advancement of human civilization, the best part of the social body, namely the brāhmaṇas, the kṣatriyas and vaiśyas (the intelligent class of men, the military class and the mercantile men) should be given special protection.
(Srimad Bhagavatam---------3:16:23--------purport).

Sūta Gosvāmī was speaking to the sages headed by Śaunaka, and therefore he addressed them in this verse as dvija, twice-born. The sages assembled in Naimiṣāraṇya hearing Śrīmad-Bhāgavatam from Sūta Gosvāmī were all brāhmaṇas, but to acquire the qualifications of a brāhmaṇa is not everything. Merely to be twice-born is not perfection. Perfection is attained when one hears the pastimes and activities of the Lord from a bona fide source.
(Srimad Bhagavatam---------3:19:33--------purport).

Whatever the father and the spiritual master order should be taken without argument: "Yes." There should be no instance in which the disciple or the son says, "This is not correct. I cannot carry it out." When he says that, he is fallen. The father and the spiritual master are on the same platform because a spiritual master is the second father. The higher classes are called dvija, twice-born. Whenever there is a question of birth, there must be a father. The first birth is made possible by the actual father, and the second birth is made possible by the spiritual master.
(Srimad Bhagavatam---------3:24:13--------purport).

King Dakṣa is addressed here by his daughter Satī as dvija, twice-born. Twice-born refers to the higher classes of men, namely the brāhmaṇas, kṣatriyas and vaiśyas. In other words, a dvija is not an ordinary man but one who has studied the Vedic literature from a spiritual master and can discriminate between good and bad. Therefore it is supposed that he understands logic and philosophy. Satī, Dakṣa's daughter, put before him sound arguments.
(Srimad Bhagavatam---------4:4:12--------purport).

One who follows the garbhādhāna saṁskāra system is actually twice-born, but those who do not, who deviate from the principles of varṇāśrama-dharma, are called dvija-bandhus. The principal occupations for a brāhmaṇa are worshiping the Deity, teaching others how to worship the Deity, studying the Vedic literatures, teaching the Vedic literatures, accepting charity from others and again giving charity to others. A brāhmaṇa should make his livelihood from these six occupational duties.
(Srimad Bhagavatam---------7:11--------summary).

This is a quotation from the Viṣṇu Purāṇa (3.8.9). As stated by Śrīla Bhaktivinoda Ṭhākura in his Amṛta-pravāha-bhāṣya, “The purport is that one can realize life's perfection simply by satisfying the Supreme Personality of Godhead.” This is also confirmed in Śrīmad-Bhāgavatam (1.2.13):
ataḥ pumbhir dvija-śreṣṭhā varṇāśrama-vibhāgaśaḥ
sv-anuṣṭhitasya dharmasya saṁsiddhir hari-toṣaṇam
“O best among the twice-born, it is therefore concluded that the highest perfection one can achieve by discharging the duties prescribed for one's own occupation according to caste divisions and orders of life is to please the Personality of Godhead.”
(Sri Caitanya Caritamrta---------2:8:58----------purport).

“Then Gāyatrī, mother of the Vedas, having been manifested by the divine sound of Śrī Kṛṣṇa's flute, entered the lotus mouth of Brahmā, the self-born, through his eight earholes. Thus the lotus-born Brahmā received the Gāyatrī mantra, which had sprung from the song of Śrī Kṛṣṇa's flute. In this way he attained twice-born status, having been initiated by the supreme, primal preceptor, Godhead Himself. Enlightened by the recollection of that Gāyatrī, which embodies the three Vedas, Brahmā became acquainted with the expanse of the ocean of truth. Then he worshiped Śrī Kṛṣṇa, the essence of all the Vedas, with a hymn.”
(Sri Caitanya Caritamrta---------2:8:138----------purport).