Time travel
Time travel is a phenomenon that is commonly addressed in science fiction. There are almost as many methods of time travel as there are science fiction authors, and multiple methods may exist in the same franchise. Consequences of time travel also vary widely: time travellers may alter history in catastrophic ways, or they may find themselves the instigators of events they sought to prevent. They may be unable to significantly effect historical events, or the may spawn various parallel timelines.
Time Travel in Star Trek
Time travel can be accomplished in Star Trek by a variety of exotic means, but the one method that is consistently available to the Federation is the so-called "slingshot effect". To accomplish this feat, a starship accelerates toward a star (or possibly a planet) at warp speed, using the star's gravity to provide acceleration greater than the ship's engines could normally provide. The ship "cracks the whip" at the closest point to the star in its course, briefly exceeding Warp 10 and initiating a time-travel effect. With precise knowledge of the ship's mass and careful control of the ship's trajectory, it is possible to direct the ship into the past or future by a specific amount of time.
Trekkie Time-Travel Arguments
Trekkie versus debaters sometimes claim that the Federation would use time travel to defeat the Galactic Empire by travelling back through time to assassinate the Emperor or otherwise prevent the Empire from becoming a threat. Such arguments typically ignore the parallel universe nature of time-travel in Star Trek: even if the Federation could successfully accomplish the objective in the past, they would merely create an alternate timeline -- nothing would change in the timeline from which the Federation launched the mission.