(covers information from several alternate timelines)
Spatial interphase, also known as interspace or an interphasic rift, was a phenomenon in which the fabric of space began to break up, allowing an overlap of parallel universes on different dimensional planes. The rift itself also contained a completely empty realm, devoid of life, between the dimensional planes.
In the mirror universe, 2155, the Tholians detonated a tricobalt warhead inside the gravity well of a dead star, creating an interphasic rift to the year 2268 of the prime universe. Unwilling to explore the rift themselves due to the dangers, the Tholians transmitted a distress call into the rift in an attempt to lure a ship from the other side. The distress call was detected by the USS Defiant which subsequently became trapped in the rift. As a result of being exposed to interphase, the crew began to suffer from a distortion of the brain tissue in their central nervous systems, which manifested itself as violent and paranoid behavior which ultimately led the crew to murder one another.
Three weeks later, the USS Enterprise arrived to investigate the Defiant's disappearance, and found it as it was fading out of the universe. Leading an away team to investigate, Captain Kirk ultimately became trapped aboard the Defiant as the Enterprise crew attempted to beam him back as the Defiant disappeared. Awaiting the next period of interphase, at which time they would be able to retrieve the captain, the Enterprise was forced to do battle with a Tholian ship. As the Enterprise fired phasers at the Tholians, the energy discharge caused the Defiant to be completely ejected from the rift into the mirror universe, but as Captain Kirk had been caught in the Enterprise's transporter beam, he was spared the shock of transition and remained trapped in the empty void of the rift between the dimensional planes in his own universe.
As the Tholians began construction of a tractor field, the Enterprise crew began to succumb to the same deteriorating mental effects of interphase as did the crew of the Defiant. Eventually, Doctor McCoy was able to counter the effects with a derivative of the Klingon nerve gas theragen. In the meantime, Commander Spock was able to successfully determine the next period of interphase, at which point they beamed Captain Kirk aboard and utilized full power to enter the rift. This had the effect of throwing the Enterprise free of the Tholians, allowing them to escape. Kirk described the rift he had entered as "a whole universe to myself, with nobody else [in it]." (ENT: "In a Mirror, Darkly"; TOS: "The Tholian Web")