I understand the ball of a foot is where the toes join with the rest of the foot. But I don't think it looks like a ball. Why is it called a "ball"?
Actually it is because it looks like a ball. It is fairly prominent in this image*:
The ball of the foot is: "The padded portion of the sole of the human foot between the toes and the arch, on which the weight of the body rests when the heel is raised."
*Image from http://www.drcomfort.com/your-feet/ball