Alternative warp was a term used by Lazarus-B to describe the negative magnetic corridor which existed between the positive and minus parallel universes. (TOS: "The Alternative Factor")
Discovery
The alternate warp was discovered at some point in the distant past by an unknown civilization. The ability to cross through the alternate warp proved that an identical parallel universe existed on another dimensional plane.
When Lazarus of the positive universe learned that another identical universe existed, this knowledge drove him insane. Opposed with the fact that he had a counterpart in the parallel universe, Lazarus went mad and attempted to destroy his counterpart, pursuing him through time and space in his ship.
Characteristics
The alternative warp appeared as a hazy corridor filled with a bluish fog, with apparent entrances on either side leading to each universe. When a living being entered the corridor, there was a momentary contact between the minus and positive universes which caused a "winking-out" effect attributed by a massive distortion of spacial laws and a momentary period of non-existence in both universes.
The alternate warp apparently had some type of feature which was referred to as a "safety valve", mainly that if two identical persons from both universes were in the corridor at the same time, the warp would only allow one to enter into the corresponding universe. Periodically, through means not entirely understood, the two beings who had entered the corridor simultaneously would switch places with each other, thereby preventing both from occupying the same space at the same time and in this way "keep eternity from blowing up"
This "safety valve" apparently did not occur if a single person entered the corridor by themselves. In this case, the person could pass through the corridor and enter the corresponding universe without difficulty. Although, standing idle in the corridor would eventually cause the person to fall through space into the alternate universe. (TOS: "The Alternative Factor")
Encounter with the Enterprise
In 2267, 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")