To bow in prayer is common in most religious practices, so it's not surprising that “to bow” in the Bible represents humility and worship in a general sense. But there are some interesting nuances. “Bowing” on its own represents only external humility and expresses the state of those motivated by truth - which tends to be rather rigid and unbending. To “bow down,” however, indicates a more internal humility, based on a desire to be good - a state which is much more flexible. Bowing with our faces to the ground has special significance. Our faces represent our interior spiritual states and the dust of the ground represents things that are profane and condemned - so bowing with our faces to the ground shows that we acknowledge the Lord's influence, and that without him we would be as profane and condemned as that dust.

To bow, as in Genesis 18:2 signifies to humble.