We should always remember that although the body of a hog is material, the hog form of the Lord was not materially contaminated. It is not possible for an earthly hog to assume a gigantic form spreading throughout the sky, beginning from the Satyaloka. His body is always transcendental in all circumstances; therefore, the assumption of the form of a boar is only His pastime. His body is all Vedas, or transcendental. But since He had assumed the form of a boar, He began to search out the earth by smelling, just like a hog. The Lord can perfectly play the part of any living entity. The gigantic feature of the boar was certainly very fearful for all nondevotees, but to the pure devotees of the Lord He was not at all fearful; on the contrary, He was so pleasingly glancing upon His devotees that all of them felt transcendental happiness.
(Srila Prabhupada's purport to SB 3.13.28)