The purpose behind bowing down while praying, to my understanding is this-
When people used to bow, they would look towards the ground and expose their necks, it's sort of symbolic for putting their life in whoever they're bowing to's hands. If, say, a king wanted to kill you, he'd take his sword and chop your head off at the neck. So when you bow, you're really saying "I'm devoting my life to you, if you don't want it, you have the power to kill me right now." So when people pray, they do the same. Or at least, that was how it started out.