The action of sucking causes endorphins ("happy" hormones) to be released. This is why, quite apart from feeling satiated, babies fall sleep at the end of a feed.
Sucking also allows the child to regain the sensation of safety they associate with it. Because feeding time is a privileged moment with mum, this explains why an upset, crying baby calms down quicker when he's sucking, whether it be from mum's breast, a bottle, his thumb or a dummy.
Incidentally, this need is so profoundly anchored in us that, even as adults, we revert back to it in other forms when faced with stress or shock. For example, when someone is in a difficult situation, one of the first things that's offered is something to drink.