A demarcation line was a political border established as part of an armistice or cease fire.
In 2259, the Gorn Hegemony established a demarcation line between the Federation and Parnassus Beta. Despite orders from Starfleet, Pike and several volunteers from the USS Enterprise were able sneak past the Gorn hunter in order to rescue Captain Marie Batel, her surviving crew of the USS Cayuga, and several colonists.(SNW: "Hegemony")