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 non-devotees, 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.
Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Third Canto, Chapter 13 – Text 28