Where did the bones of the middle ear come from?

The reptilian jaw joint. In reptiles the jaw hinges on two bones, the quadrate and the articular; in mammals it hinges directly on the skull, and those two bones have migrated into the ear to become the anvil and the hammer. We hear with a repurposed jaw joint.

This is one of the best-documented transitions in the fossil record, because the change happened in stages that are all preserved. There are fossil forms with both joints working at once - the old reptilian hinge and the new mammalian one side by side in the same skull - which is exactly what a transitional stage should look like and is unusually cooperative of the evidence. It also happens again in embryos: the bones form in the developing jaw region and move.

The result is a lever system that solves a real physical problem. Sound reaching a fluid-filled inner ear from air would mostly reflect off, because the two media are so different, and the three bones amplify the pressure by something like twentyfold to force the energy across. Which is why a mammal hears high frequencies far better than a reptile does, and why the bones are fully grown at birth and never change size.