The Lord is spoken of herewith as the origin of the boar species. As stated in the Vedānta-sūtra (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 ādi, or the beginning. In Bhagavad-gītā Arjuna addresses the Lord as ādyam, or the original. Similarly, in the Brahma-saṁhitā the Lord is addressed as ādi-puruṣam, the original person. Indeed, in Bhagavad-gītā (BG 10.8) the Lord Himself declares, mattaḥ sarvaṁ pravartate: "From Me everything proceeds."
In this situation the Lord assumed the shape of a boar to kill the demon Hiraṇyākṣa and pick up the earth from the Garbha Ocean. Thus He became ādi-sūkara, the original boar. In the material world a boar or pig is considered most abominable, but the ādi-sūkara, the Supreme Personality of Godhead, was not treated as an ordinary boar. Even Lord Brahmā and the other demigods praised the Lord's form as a boar.
This verse confirms the statement in Bhagavad-gītā 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 Hiraṇyākṣa He fulfilled His promise to kill the demons and always protect the demigods headed by Brahmā. 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 Vṛndāvana, 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 akhaṇḍitotsavam. 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 Vaikuṇṭhalokas, the abode of the Lord, who is worshipable even by demigods like Brahmā, 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 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.