American football is a contact sport where two teams of 11 men compete by attempting to gain possession of the ball and score points. After 60 minutes, the team with the most points wins.
Points can be scored by running the ball past the other team's goal line, catching a throw beyond the goal line or by kicking the ball through the opponent's goal posts. Tackling the other team's ball carrier behind their own goal line can also score points, although this rarely happens.
As you can see, the ball is needed in all instances to score points. Initial possession is determined by a coin toss, and then a kick off. The kick off is done to transfer possession of the ball between teams.
Here is an example of a kick off and return resulting in points, although most don't: