An energy barrier is a natural or artificial energy phenomenon that impedes movement through it.
In 2371, the USS Olympia discovered an energy barrier around a planet and initiated a scan. This led to a quantum reaction which damaged the Olympia and sent the ship spiraling towards the planet surface. Captain Lisa Cusak sent out a distress call, which the energy barrier redirected three years into the future. (DS9: "The Sound of Her Voice")
The Gamma Quadrant planet Gaia had an energy barrier around it. When it was discovered by the crew of the USS Defiant in 2373, they detected lifeforms on the surface. The interference of the energy barrier was increasing and Jadzia Dax predicted it would soon become impassible.
The Defiant later entered the barrier where the crew discovered the inhabitants of the planet were their descendants. After interacting with them, and learning that if they did not enter the energy barrier in the same way, the Gaians would cease to exist. Yedrin Dax convinced them that his plan to create two Defiants, one which leave and one which would be sent back in time, would work.
The crew later discovered the plan was a fabrication, and no duplicate Defiant would be created. The crew later resigned themselves to their fate, but the future version of Odo changed the starship's flight plan and the Defiant successfully passed through the energy barrier. (DS9: "Children of Time")
In 2374, the Defiant detected Captain Cusak's distress call and began a rescue mission. They later discovered Cusak had been dead for three years and that the barrier had sent it into the future. (DS9: "The Sound of Her Voice")
There is a tetryon-based energy barrier in place on the southern continent of Ledos, placed by Species 312 to protect the territory of the Ventu from the more advanced Ledosians. A shuttlecraft from the USS Voyager, carrying Commander Chakotay and Seven of Nine, accidentally crashed into the barrier in 2378. While inside, Seven was able to disrupt the barrier's source by generating a dampening field with the shuttle's deflector, allowing their rescue. However, the Voyager crew elected to remove the deflector and restore the barrier afterwards due to the damage that might result if the Ledosians were allowed to interact with the Ventu. (VOY: "Natural Law")