Homecoming is a school tradition (high school and college). It's a home football game accompanied by homecoming week. What homecoming week includes depends on the school. At my high school we got to dress up every day of the week and there was a powderpuff football game (girls only football game for fun). There was also a dance after the game and a parade before.
Here we have games on Sunday, a homecoming king and queen competition, an after-party after the game, and a bunch of other stuff.
A homecoming float is a float pulled on a trailer behind a car. Usually there's a theme and it almost always is related back to beating whoever your football team happens to be playing in the homecoming game.