Though there are several brands, battery terminal pullers all work on the same principle and basically are similar to "gear" pullers, except smaller.

They have a couple of "fingers," the tips of which grip underneath the bottom edge of the loosened battery terminal to be removed, and they have a threaded rod [acts like a push rod] which contacts the top of the battery terminal.

When the finger "tips" are hooked beneath the terminal clamp, and the pusher/plunger is screwed inward, the fingers are pulled upward, pulling the battery terminal with them.

To prevent damage to the battery terminal, the terminal clamp, and the puller it is critical that the locking screw of the terminal clamp be completely loosened before attempting to pull the clamp.