A temporal explosion is a detonation in the fabric of space-time, capable of destroying an entire star system. A temporal explosion could be caused by the improper use of the time drive aboard a timeship.
In one timeline, the 29th century Sol System was destroyed by this anomaly. It was caused by Henry Starling's use of Captain Braxton's Federation timeship Aeon from 1996 in a secondary alternate timeline. Fortunately, this tragedy was averted by Starling's destruction by the crew of the USS Voyager, before he could attempt the time jump. (VOY: "Future's End", "Future's End, Part II")