SB 3.19.31
maitreya uvaca
evam hiranyaksam asahya-vikramam
sa sadayitva harir adi-sukarah
jagama lokam svam akhanditotsavam
samiditah puskara-vistaradibhih
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
Sri Maitreya continued: After thus killing the most formidable demon Hiranyaksa, the Supreme Lord Hari, the origin of the boar species, returned to His own abode, where there is always an uninterrupted festival. The Lord was praised by all the demigods, headed by Brahma.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The Lord is spoken of herewith as the origin of the boar species. As stated in the Vedanta-sutra (1.1.2), the Absolute Truth is the origin of everything. Therefore it is to be understood that all 8,400,000 species of bodily forms originate from the Lord, who is always adi, or the beginning. In Bhagavad-gita Arjuna addresses the Lord as adyam, or the original. Similarly, in the Brahma-samhita the Lord is addressed as adi-purusam, the original person. Indeed, in Bhagavad-gita (10.8) the Lord Himself declares, mattah sarvam pravartate: “From Me everything proceeds.”
In this situation the Lord assumed the shape of a boar to kill the demon Hiranyaksa and pick up the earth from the Garbha Ocean. Thus He became adi-sukara, the original boar. In the material world a boar or pig is considered most abominable, but the adi-sukara, the Supreme Personality of Godhead, was not treated as an ordinary boar. Even Lord Brahma and the other demigods praised the Lord’s form as a boar.
This verse confirms the statement in Bhagavad-gita that the Lord appears as He is from His transcendental abode for the sake of killing the miscreants and saving the devotees. By killing the demon Hiranyaksa He fulfilled His promise to kill the demons and always protect the demigods headed by Brahma. The statement that the Lord returned to His own abode indicates that He has His own particular transcendental residence. Since He is full of all energies, He is all-pervasive in spite of His residing in Goloka Vrndavana, just as the sun, although situated in a particular place within the universe, is present by its sunshine throughout the universe.
Although the Lord has His particular abode in which to reside, He is all-pervasive. The impersonalists accept one aspect of the Lord’s features, the all-pervasive aspect, but they cannot understand His localized situation in His transcendental abode, where He always engages in fully transcendental pastimes. Especially mentioned in this verse is the word akhanditotsavam. Utsava means “pleasure.” Whenever some function takes place to express happiness, it is called utsava. Utsava, the expression of complete happiness, is always present in the Vaikunthalokas, the abode of the Lord, who is worshipable even by demigods like Brahma, to say nothing of other, less important entities such as human beings.
The Lord descends from His abode to this world, and therefore He is called avatara, which means “one who descends.” Sometimes avatara is understood to refer to an incarnation who assumes a material form of flesh and bone, but actually avatara 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 avatara.