Matthew White wrote:
My sensei's replace that phrase with "get your center behind your hands". Keeps us from trying to "do stuff with our arms" and use good body movement instead.
This is excellent advice. After doing aikido for a while, is hard to remember how obscure the notion of one's "center" seemed at first. As a first approximation, think of it as being in front of your navel (although higher or lower is OK). Another minor point is that techniques often work easier if the point of contact with the opponent (e.g. the grabbed wrist), rather than your hand, is in line with your center.