(covers information from an alternate timeline)
Elysia was a small alternate universe, a parallel time continuum, that periodically touched the prime universe in the Delta Triangle region of the galaxy. Elysia was more aptly described by Devna, as "a pocket in the garment of time." The collisions between the two alternate universes produced time warp vortexes in the time barrier between the universes. The warps allowed passage from one side to the other at high warp speed.
Elysia was governed by the Elysian Council. Its "starship graveyard" contained all of the ships lost in the Delta Triangle over the millennium preceding the arrival of the USS Enterprise in 2269. While time passed at the same rate, the effects of time, like aging, occurred at an extremely slow rate in Elysia relative to the outside universe. All acts of violence were forbidden in Elysia, and were stopped by the members of species with psionic powers. Captain James T. Kirk noted that "Elysia is, in many respects, a perfect society. But with all its virtues, it is not home. And home, with all its faults, is where we prefer to be." (TAS: "The Time Trap")
According to the Star Trek: Department of Temporal Investigations novel Forgotten History, the "time standing still" in Elysia was an effect caused by actions requiring less energy there. This caused aging to be slower and healing mechanisms to be more effective. It was also theorized this effect might even be responsible for the more peaceful society, because even thoughts took less effort, making it easier to come up with better solutions. By 2383, travel back and forth between the prime universe and Elysia had been accomplished again, although Elysians did not engage in it.