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.