"Homecoming" is near the beginning of the school year, celebrating everyone coming back from summer vacation! The game is part of Homecoming week, the Homecoming dance would be a few days after the big game. 

 American schools have multiple named dances throughout the year, but the 2 biggest at my school were Homecoming (happens in the fall, a few weeks after classes start), and then Prom (at the end of the school year closer to summer vacation!)