It always amazes me that for some reason coaches at the youth level many times put the non-athletic player (i.e. usually big and slow - sorry thats probably not PC) when in fact it is a very important position at all levels.
My son does a drill where he puts one ball in front of the plate and one on either side about 2-3 feet to the left and right. He imagines blocking the middle one then POPs up (no hands) and goes to the left, then middle, then right, then left, etc. After about a minute he is sweating big time.
Another drill he does for quickness is he is in the catchers position - one man in front of him, one behind - 7-8 yards or so. The man in front throws the ball in the dirt, he blocks it, tosses ball to the side and rotates 180 degrees (again its a POP up to the catchers position and spin - no standing up or using hands) where the other guy throws in the dirt as well. This is done very agressively - its bang, bang, bang. This continues for at least a minute and again he is sweating big time.
We all get hung up on the throw out to second, which is great, but the catchers primary job is stop/catch the ball.