A temporal inversion was a phenomenon associated with time travel and changes in the timeline.
29th century timeships initiated a temporal inversion as part of the process of generating a temporal rift. Such a procedure was carried out by Henry Starling in 1996 of an alternate timeline, when preparing to take the Federation timeship Aeon to the future. Upon the initiation of the inversion, the Aeon's temporal field generator of its temporal core powered up to cascade potential, and the rift was generated. (VOY: "Future's End, Part II")
In an alternate timeline, in 2390, Harry Kim and Chakotay used a stolen Borg temporal transmitter to send a message back in time to the year 2375, in order to save the starship USS Voyager, which had been destroyed in the Takara sector while attempting to utilize quantum slipstream drive to return to the Alpha Quadrant. By sending a new set of phase corrections to Seven of Nine's interplexing beacon, they were able to successfully change history by causing the slipstream to collapse, returning Voyager to normal space before the crash. (VOY: "Timeless") This alteration to history constituted a temporal inversion, the effects of which Captain Braxton, a Starfleet officer from the 29th century, had to repair. (VOY: "Relativity")