This is a term used in football to describe an event in which a team gains possession of the ball after it was lost via fumble or interception. The team gaining possession of the ball may be the same team that fumbled the ball. The action of "recovering" the football only describes the act of gaining possession, it does not matter which team previously had legal possession. A team cannot intercept its own pass, so it could only recover an interception if the intercepting team then fumbled the ball. The term is sometimes used mistakenly in football to describe all change in possessions.
Although confusing, the term recover applies to either team recovering a fumble because the ball is officially live once fumbled. In other words, once a team fumbles the ball, they no longer have possession. Since they no longer have possession, they may, "recover," the ball. Since the opposition has an equal chance of gaining possession of the ball, they too, may recover the ball. For example, "The team recovered the fumble after it fell to the field."