Drake Baer for The Science of Us: 

The University of Chicago psychologist Susan Goldin-Meadow has spent much of her career trying to grasp (yes, pun intended) what’s happening when people talk with their hands. As Goldin-Meadow defines it, “co-speech gesture” is different from action, like grabbing a cup of coffee or combing your hair, and it’s different from movement for movement’s sake, like in dance, ritual, or exercise. The gestures that hearing people make are also quite different from sign language; in signing, Goldin-Meadow says, there are distinct units of expression, and signs only relate to other signs. But with gesture, hand movements blur together, and they only really make sense relative to what someone’s saying. “Gesticulation isn’t divorced from speech. It’s completely tied to your speech,” Goldin-Meadow tells Science of Us. “It’s part of your cognition. It’s not just mindless hand-waving.” Researchers haven’t yet pinned down exactly how this connection works, but Goldin-Meadow believes part of it is that gestures reduce what psychologists call “cognitive load,” or the amount of mental energy you’re expending to keep things in your working memory.

All those times I've said that I'm thinking with my hands turn out to be true.