Your kitten is playing with your hands and fingers. Anything that moves is open game for them. A cat will do the exact same thing with a mouse - play with it, toss it around, claw at it, lick it. Chances are, the attack won't kill the mouse, it'll have a heart attack. Basically, he or she is practicing on you to hone hunting and killing skills. The bites and clawing kills or maims. The licks will remove skin and muscle from the bone. Ever wonder why a cat's tongue is rough? That's why.
It's important to teach your cat that your hands aren't playthings. Kitten bites can hurt especially if they get hold of your webbing between your thumb and forefinger or the soft pads of your hands beneath the fingers and clawing can make your hands look like you belong in the psych ward.
Edit: Oh, I didn't read the whole thing. Not your hand but other kittens (?). Still valid, though. Anything that moves the kitten or cat will pounce and attack.