The Official Baseball Rules defines a Force Play: A FORCE PLAY is a play in which a runner legally loses his right to occupy a base by reason of the batter becoming a runner.
Well, a force play rule can cause a great deal of confusion because the term “force play” is commonly misunderstood to mean any play in which the defense tags the base for an out. For example, the batter hits a line drive at F4 who then throws to F3 to double up R1. An announcer may say that R1 was forced out at first. But that is incorrect, since R1 did not legally lose his right to occupy first base due to F4 catching the ball and retiring the batter runner.
The force out is so called because the runner is forced to advance when the batter becomes a runner. Another example: bases loaded, two outs. The batter grounds the ball to the third baseman who tags R2 after R3 has crossed the plate. This is a force out and the run does not count because R2 is forced to advance when the batter becomes a runner. Rule 7.08(e) states that a runner or his next base may be tagged when the runner is forced to advance.
A force play cannot occur when a batted ball is caught for an out. The batter is out and no runner legally loses his right to occupy a base by reason of the batter becoming a runner. A batted ball caught for an out often creates a time play situation. Example: R3, R1 stealing, one out. The batter hits a fly ball to F8 who catches it for the second out. R3 tags and crosses the plate, before F8 throws to F3 to double up R1 for the third out when he failed to tag. This third out is a time play, not a force play. Since R3 crossed the plate before the defense doubled up R1, R3’s run counts. Here is a video example. [Unfortunately, the MLB umpire crew misapplied the rule in this case and discounted the run. Then, realizing their mistake three innings later, placed the run back on the board. Read about what happened here.]
A force play can be removed when the runner is no longer forced to advance. Rule 7.08(e). For instance, bases loaded, no outs. The batter hits a line drive to F5 who drops the ball. F5 then steps on third base to force out R2 and throws home. F2 tags home plate. However, R3 is not forced to advance and must be tagged. Since F2 did not tag R3, he scores. Here is the video of this play.
A force play can also be reinstated if the runner advanced past a base, and then retreats back by retouching the base. Rule 7.08(e). For example, in this video clip R1 is stealing and acquires second base. The batter hits a base hit to right, but R1 believes the ball is caught, retouches second and retreats to first base. By retouching, R1 has reinstated the force play and is forced out a second base.
A force may be removed when a following runner passes a lead runner, as in this video clip. The lead runner must now be tagged once the force is removed.
Once an infield fly is called, the batter is out and there is no force play. Runners may advance at their own peril and must be tagged. Here is a video example of this situation.