Pyramid Head (from SH2) is or can be several things:
a.) The embodiment of James' suffering and/or guilt.
b.) The embodiment of James' sexual frustration with his dead wife. This would explain his gestures of dominance over the more feminine creatures of Silent Hill 2 (i.e. 'raping' other monsters)
c.) An executioner of sorts; some believe he is The Red God, Xuchilbara.
-A common theory is that Pyramid Head is Jimmy Stone. Jimmy was the leader of the Valtiel sect of The Order; often he is seen wearing a red, triangular hood during ceremonies. He was called "The Red Devil" by some. This leads many to believe Pyramid Head is Jimmy Stone.
Pyramid Head is one of the four things above.