I don't even think Pyramid Head has an actualy story behind it. In Silent collina 2, it is a voilent monster, which betrays James' 'other half' o something?
In Silent Hill: Homecoming, he acts as a judge o some sorts. If a person 'deserves to die' (in his eyes), it'll hunt down that person and kill him.
And as for the helmet... PH's creators wanted a 'humanlike' monster with a mask on. But then they realized it would be nothing più then a man wearing a mask. They decided to give PH a casco shaped più like a triangle, to make it look più disturbing. With sharp edges, etc etc, to hurt PH itself wearing it. Once te wear the helmet, te can't take it off, and your a Pyramid Head.