From BR Bullpen

A tag is the act by which a fielder applies the ball against a baserunner or the batter-runner in order to put him out. The runner is automatically out if he is tagged with a live ball while not in contact with a base.

Certain situations require that the out be made via a tag, while others do not (see: force play). In general, when a baserunner has a choice whether to advance to the next base or not, and is not forced to do so by the situation, a tag is required. For example, a tag is required to retire a baserunner on a stolen base attempt, on a pick-off, on a runner trying to advance an extra base on a base hit, or trying to advance on a ground ball when there is an unoccupied base between him and the batter-runner. A tag is not required on a force play, or when a batter is returning to his base after a fly ball has been caught.

In certain cases the force can be removed during the course of a play, requiring a tag on a play which would normally be a force play. The most common example of these is on a reverse double play. For example, with a runner on first base, the batter hits a ground ball to the first baseman. If the first baseman throws immediately to second base, it is a force play and no tag is required; however, if he first touches the bag or tags the batter to put him out, then the runner could choose to return to first base, as it is now unoccupied. If the first baseman then throws to second base, the runner must be tagged to be put out.