Someone who is older than you, or higher than you. Translated it means senpai in japanese.
"He greatly respects Mamoru, who is an upperclassman at his school."
Any student in a high school other than a freshman. These students are usually pretty normal, but for some of them, the evolution from frosh to non-frosh makes them into total jackasses. These jackass-upperclassmen should be avoided by freshmen at all costs.
Upperclassman: Hey, you're a freshman, right?
Freshman: Uh ... yeah?
Upperclassman: Go clean the floor with your tongue.