Normal is somewhat of a catch all type, given to moves that either don't have a particular connotation with any of the other types or are so basic as to be "normal" from our perspective. This makes normal type moves extremely common, as they are so basic that it is "normal" for Pokemon to learn them. I mean, its not really hard to learn how to tackle or pound something in the real world, so for a magic elemental animal its probably a cakewalk. Finally, as stated above Normal's a "catch all" type consisting of a variety of moves from Splash to Transform to Judgement to Giga Impact, so many moves that Pokemon learn don't necessarily have "normal" connotations, but are just given the type because they don't fit any other well. Simply put, it is "normal" for Pokemon to learn normal type moves.
Hope this helps