ANSWER: The Biblical verse concerning the body of Moses you have questions about is located at verse 9 of Jude 1 (Jude only has one chapter).
But Michael the archangel, when he was personally taking issue with the devil, disputing about the body of Moses, did not presume to pronounce a reviling judgment against him . . . (Jude 1:9)
There exists a variety of interpretations in Biblical commentaries regarding this event involving the dead body of Moses. Many of them seem, on the surface, to be correct. On closer inspection, however, they are found to be completely false. For example, one commentary assumes God needed the body in order to resurrect him sometime before he appeared in the Transfiguration of Jesus.
In the transfiguration explanation, the devil argues that the body should be left in the ground in an effort to somehow thwart God's plans. This argument is groundless since NO ONE, not Moses, Elijah, King David and countless others, have yet to be resurrected from the dead or gone to heaven (except Christ, see article on the first resurrection).
The true Biblical explanation is as follows. The first of the Ten Commandments states that we are to have no other gods before the true God (Exodus 20:1 - 3). Satan, always looking for ways to deceive humans, wanted to make the body of Moses and his grave an object of worship.
Israel had formally been guilty of worshipping the golden calf (see Exodus 20 and 32), and the body and tomb of Moses, the revered leader of the nation, would have been a constant place of visit by the people of Israel, had they known the location of his body. People today do similar things, such as Russia having a public tomb for Stalin and Lenin. Many countries like the United States have a tomb for the 'unknown soldier,' and so on where people go today and dwell on the past.
Memorials force us to dwell in the past, rather than dwelling in the present and going on with our lives. Some people worship these types of memorials as icons. God wants our worship to be only of Him, instead of some shrine to remind us of the past. Satan will use anything he can, even the body of Moses, to try and direct the focus of human minds away from God and onto something that is physical and temporary.