Although he has the same name, this is not the creature from the Silent Hill series. Pyramid Head is a boss fought in (usually) pyramids, though that is mainly in name only. His first appearance is in War of the Worlds II: Time Travel, where he attacked far after the pyramid level. However, he does claim rights to every pyramid, and thus usually fights the party there.
It is unknown whether or not if Pyramid Head is living. He looks like a humanoid, but his base shape covered in triangles, including his head. He also has two huge fists. It may be suspected that he is related to Fist foxes, but that is unknown.
Pyramid Head has a great, brick-like defense, and an earth-based offense. In at least one game, you were required to push him backwards off of the pyramid to defeat him.