One of the things I love about signing is that my older kids position baby's hands to make her say things. You can't do that with their vocal chords. A skeptic might say that's not real communication. But the reason we call Mothers "Ma" and Fathers "Da" are because those are some of the first sounds a baby makes, and we added meaning to them.
So a baby clutching it's fist is just something a baby does. If you give them milk every time they do it, they make a connection. And then they have the power to ask for something using a gesture they can make.