Caturvyūha or Chatur-vyūha ("Four emanations"), is an ancient Indian religious concept initially focusing on the four earthly emanations (Vyūhas) of the Supreme deity Nārāyaṇa (or Vishnu). The first of these emanations is the hero-god Vāsudeva (or Vāsudeva-Krishna), with the other emanations being his kinsmen presented as extensions of Vāsudeva himself.
The four earthly emanations, or "Vyuhas", are identified as Vāsudeva-Krishna (son of Vasudeva* by Devaki), Samkarshana (Balarama-Samkarshana, son of Vasudeva* by Rohini), Pradyumna (son of Vāsudeva-Krishna by Rukmini), and Aniruddha (son of Pradyumna).
* Vasudeva Anakadundubhi, king of the Vrishnis in the region of Mathura.
The Chatur-vyūha forms of Vishnu are related to four of the six causes of creation which six are God Himself as the final cause of creation and His five aspects – Narāyana ('thinking'), Vāsudeva ('feeling'), Samkarśana ('willing'), Pradyumna ('knowing') and Aniruddha ('acting') successively; each divinity controls its specific creative energy.
The Mahabharata, Book 12: Santi Parva: Rajadharmanusasana Parva: Section XLVIII (extract) :
Thou art the Lord of those that are bound to thee in faith. O God, thou art adored (by the faithful) under four excellent, high, and secret names*.
* Note from Kisari Mohan Ganguli : The four names under which the Supreme Being is adored by the faithful are Vasudeva, Sankarsana, Pradyumna, and Aniruddha.
The Mahabharata, Book 12: Santi Parva: Section CCCXL (extract) :
That illustrious one, viz., Vasudeva, who is called Kshetrajna, and who is freed from attributes, should, O king of kings, be known as the puissant Sankarshana, when he takes birth as Jiva. From Sankarshana arises Pradyumna who is called 'He that is born as Mind.' From Pradyumna is He who is Aniruddha. He is Consciousness, He is Iswara (Supreme Lord).
Note from Kisari Mohan Ganguli : This cosmogony is agreeable to the Vaishnava scriptures. Above all, without beginning is Vasudeva. From Vasudeva is Sankarshana. From Sankarashana is Pradyumna. From Pradyumna is Aniruddha.
The Mahabharata, Book 12: Santi Parva: Section CCCLII (extract) :
The person who realises that inconceivable Purusha and comprehends his subtile existence in the quadruple form of Aniruddha, Pradyumna, Sankarshana, and Vasudeva, and who, in consequence of such comprehension, attains to perfect tranquillity of heart, succeeds in entering into and identifying himself with that one auspicious Purusha.