A fumble is when anyone who has possession (or is gaining possession) of the football mishandles it and loses it as a result. You may have heard of quarterbacks “fumbling the snap,” which is really a joint effort between the center and the quarterback to not get the snap off correctly. Fumbles can also occur when a ball carrier gets distracted or loses his grip or runs into any set of circumstances in which he loses possession of the ball after he has it. There are also forced fumbles, which occur when a defensive player causes the impetus for the fumble, usually by punching the ball out from behind.
Not all fumbles are turnovers. If the other team recovers the fumbled ball, it is a turnover. But if the team previously in possession recovers the ball – like if the snap is fumbled but an offensive linemen jumps on it to recover it – then they keep possession of the ball. It is not a turnover. It is cause for celebration.