A jailbreak or prison break was an attempt to escape from the custody of one's captors.
In 2153, Kessick refused to give Trip Tucker the wanted coordinates of his homeworld unless he could free him. Tucker initially refused, saying he and Jonathan Archer hadn't come to start a prison break. (ENT: "The Xindi")
In 2270, Leonard McCoy initially balked at being broken out of jail on Dramia II by Spock until the Vulcan informed him that the potentially fatal Dramia II plague was affecting members of the USS Enterprise's crew, necessitating McCoy's help to formulate a cure. (TAS: "Albatross")
In 2287, shortly after blowing the wall of the USS Enterprise-A brig wide open to allow McCoy, Kirk, and Spock's escape, Montgomery Scott asked them why they were still standing around inside the cell, adding, " Do you not you know a jailbreak when you see one?"(Star Trek V: The Final Frontier)
In 2369, as incentive for the Nol-Ennis and Ennis combatants to stop fighting and discuss a ceasefire, Benjamin Sisko promised them transport off the moon they were currently living on. When Julian Bashir compared Sisko's offer to "assisting a jailbreak", Sisko explained that he felt they had more than paid for the crimes that had condemned them to the moon. (DS9: "Battle Lines")