The team that has the ball starts with it at a certain point on the field. The first ten yards between where they are and the goal line is divided. The offensive team now has 4 opportunities, or "downs," to advance the ball, otherwise the team on defense will get it from there. If they are successful in advancing the ten yards in 4 downs or less, they get another 4 downs to advance at least another 10 yards. This repeats until they reach the goal line or fail at advancing the necessary yardage. The following flow chart demonstrates the average game play for the team with the ball. The defense is trying to stop them at all times.
When the offense is close to the goal posts and they are on their 4th and final down, they may chose to attempt a field goal. Worth less than a full score, it's better than turning the ball over on downs. If they are not close to the goal posts, when they reach 4th down they can punt the ball to the other team.