Alternative warp was a term used by anti-Lazarus to describe the negative magnetic corridor which acted as a "safety valve" between the positive universe and the parallel universe he was from, the minus universe. (TOS: "The Alternative Factor")
At some unknown point in the distant past, Lazarus's people in the minus universe discovered a way to traverse the alternative warp and explore the positive universe. When the Lazarus of the positive universe learned of his counterpart's existence, he went mad, unable to bear the thought of it. This Lazarus attempted to destroy his counterpart, pursuing him through time in his ship, eventually arriving in the year 2267.
At that point, their constant transits through the alternative warp caused a cosmic "winking-out" effect centered on the surface of a planet which the USS Enterprise was investigating. Captain Kirk learned that, if the two versions of Lazarus were ever to meet, they would annihilate each other as matter and antimatter do, causing a complete destruction of both universes. Eventually, with the assistance of the Lazarus from the minus universe, Kirk was successful in trapping both of them in the alternative warp and destroying Lazarus's ship, thereby trapping them inside for eternity. (TOS: "The Alternative Factor")