The incarnation of the Supreme Personality of Godhead is not forced to act by the material laws of nature. The word sveccha is used here to indicate that He appears out of His supreme will. The conditioned soul is forced to accept a particular type of body according to his karma given by the laws of material nature under the direction of the Supreme Lord. But when the Lord appears, He is not forced by the dictation of material nature; He appears as He likes by His own internal potency. That is the difference. The conditioned soul accepts a particular type of body, such as the body of a hog, by his work and by the superior authority of material nature. But when Lord Krsna appears in the incarnation of a boar, He is not the same kind of hog as an ordinary animal. Krsna appears as Varaha-avatara in an expansive feature which cannot be compared to an ordinary hog's. His appearance and disappearance are inconceivable to us. In the Bhagavad-gita it is clearly said that He appears by His own internal potency for the protection of the devotees and the annihilation of the nondevotees. A devotee should always consider that Krsna does not appear as an ordinary human being or ordinary beast; His appearance as Varaha-murti or a horse or tortoise is an exhibition of His internal potency. In the Brahma-samhita it is said, ananda-cinmaya-rasa-pratibhavitabhih: [Bs. 5.37] one should not mistake the appearance of the Lord as a human being or a beast to be the same as the birth of an ordinary conditioned soul, who is forced to appear by the laws of nature, whether as an animal, as a human being or as a demigod. This kind of thinking is offensive.

From Srila Prabhupada's purport to SB 4.8.57