It's crazy how much you don't actually need to look at your hands. I learned juggling a long time ago, and I remember discovering this. It feels like you become good at predicting from the top of the arc where you need to place your hand so that it intersects with the arc. I was surprised to see that as I got better, I also started catching the balls where the throw was a little off and I had to extend my arm to catch it, but still without actually looking at my hands. And at some point it becomes automatic and fast.

There was this one time when I was grocery shopping (I had been practicing a lot at that point), and someone accidentally pushed a jar off a shelf, and I caught it without looking or even thinking. I felt a little bit like a super hero with super reflexes :-)