While aboard the Defiant in the Gamma Quadrant, the DS9 crew is surprised to see a planet suddenly materialize right in front of them. The inhabitants of the planet invite the crew down for a visit.
The planet is called Meridian, and it spends most of its time in another phase of existence, where its people exist only as consciousness, with no physical being. The planet is in this dimension for a very short time. In twelve days it will disappear for sixty years. Each time it returns, the planet will have less time in this universe, and eventually will stop appearing.
The crew offer to help stabilize the planet so that it will not disappear forever. Jadzia Dax is distracted from her analysis of the problem by one of the Meridian people, a man named Deral. They have begun to fall in love. He tells her he will leave the planet and come with her instead of returning to the other phase. His people are not happy to hear this, because they have a very small population and cannot lose a member. To help them, Dax decides to stay on Meridian. She works quickly to find a way to alter her molecular structure so that she can slip into the other dimension along with the planet and its people. She is also able to help the crew stabilize the planet enough so that although it will still shift phases, next time it will stay in this universe for 30 years.
Time runs out, and Dax bids a tearful goodbye to her crewmates aboard the Defiant. She returns to Deral and waits with him for the phase shift. As the planet begins to shimmer out of the universe, she is wrenched by a force. Her body is not pulled out of phase with Deral's. She is stuck between dimensions, and, worse, is holding the entire planet there with her.
The crew beams her back to the ship, saving her life. Meridian slips safely into its other dimension. Dax returns to her bunk to be alone and begin the 60-year wait before she can again be with Deral.
This episode also features a subplot involving a DS9 visitor called Tiron (Jeffrey Combs, in the first of many Star Trek appearances), who employs Quark to make him a custom holosuite program featuring a holographic Kira. Quark tries multiple times to get enough data on Kira to make the hologram, and eventually breaks into secure files to accomplish this. Odo and Kira discover the security break, and have a little fun at Quark's expense, by altering the holographic Kira's head to that of Quark's.
The plot of this episode is reminiscent of the musical Brigadoon, in which a Scottish village appears for one day every hundred years.