Human, ergo insignificant (unless you're Bella Sue, that is). He was one of Charlie's best friends. His only importance to the story line is to keep Charlie out of the way in Twilight, and to provide a funeral for confusion with Bella's in New Moon . Unfortunately, another one of Charlie's friends was murdered in the movie version of Twilight, so that means he will lose two friends in a span of two books. Poor guy.
shit-fest movie adaption of New Fail Moon, Harry dies of a heart attack brought on by Victoria who was out for Smella's blood during that time. Victoria lifts him off the ground by his shirt, and he has a heart attack from his old age (right after totally shitting his pants). So Harry is now dead (Bite my ass, movie). Not many people really care, though, because he wasn't Bella and therefore wasn't speshul enough to matter. Oh well, at least him dying took away any chance Meyer had to ruin his character.