This is a term used in football, and other sports, to describe who has the ball. It can also be used to describe how long a team/player has/has not had the ball. In a football game, the team who has the ball is on offense. They have "possession" of the ball. If they fumble or otherwise lose the ball, it is called a turn-over and they lose possession of the ball.
The term is usually used to refer to offense, but could be used on defense, such as "defensive possession." This would be used to describe how long a team is on defense. If one replaces offensive in the above phrase, it would describe how long a team had the ball on offense.
The term could also be used to count the number of times a player or team has the ball on offense or defense. This would be phrased as the, "number of possessions." In order to be a successful, a football team must have possession of the ball long enough to score more often than their opponent. The best teams do not need lots of time to score, but are also capable of holding onto possession of the ball in order to keep it out of the hands of the other team. They do this through clock-management and not turning the ball over.