A celebration, usually held during the fall football season, when high schools and colleges hold events to welcome former students and alumni who have come back for a visit. Most events usually revolve around current students, especially the homecoming football game, the homecoming bonfire, homecoming dances, etc. The alumni might get to go to dinner together, they might have a dance (playing a lot of old music that hasn't held up well), they might have a reception, they'll probably drink more than they should've.

For current students, Homecoming is Prom, Jr.; for alumni, it's nearly always pure disappointment.

Addendum: sekicho says homecoming "generally means that the team is coming home after a series of away games." Well, I'm not so sure about that. I seem to remember homecomings that directly followed home games. But that may indeed where the custom stems from...