It is a single game.
It is also hard to explain clearly in writing.
There's a field. The object of the game is to get the ball to your end of the field. When you do, you score points - it can be anywhere from 1-6 points, depending on how, exactly, you got the ball to your end of the field. The other team is, of course, trying to stop you and get the ball to their end of the field.
Unlike soccer, it isn't continuous play. The game stops and starts very, very frequently.