In the US, there is usually one major (American) football game at the high schools that is designated as "homecoming." Often alumni come back for this game. There is usually a homecoming dance associated with it, and a homecoming king and queen, as well as the homecoming queen's court.
The short answer is: A major social event for high school students.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.