The cat’s claw is the part of a pry bar that is used for pulling nails. It has a notch that fits around the stem of the nail, and if wedged under the head of the nail allows one to apply leverage to pull the nail out.
There is also a tool called a cat’s claw, which looks like a claw hammer with the hammer head removed. It has a straight shaft that curves into a claw, ending in two sharp points. The points are sharpened so that it can be driven into the wood, allowing you to get under the heads of nails that have been driven in flush with the surface of the wood.
Cat’s claws tend to give you better leverage than you would get with a claw hammer, can fit into awkward spaces better (due to the lack of a head), and are smaller and easier to use than a crow bar or pry bar.