The Brig was a term for a naval or military prison or jail on a ship or base.
During the Second Robotech War, Dana Sterling's practice drill gone wrong lead to her being thrown in The Brig to reconsider her behavior in solitary confinement. Later, Dana was berated by Colonel Alan Fredericks. She had not exercised conduct becoming either an officer or the daughter of war heroes. After she begged for another chance, Fredericks agreed to give her one more opportunity to prove herself. Dana was released in time to lead her squad into their first official combat. (Masters Saga: "False Start")
Bowie was once caught at Piano & Bar by a GMP Officer, who took him to Nova Satori, who was very upset at his actions at the bar. Dana agreed to take responsibility and look after Bowie.
The next day, the night before a large mission wherein the 15th Alpha Tactical Armored Corps would be infiltrating the Tirolian Mothership which had crashed near Monument City, Dana suggested that Bowie go to the bar to play the piano. There, Bowie was insulted by a man at the bar, and was involved at a brawl. For this, he was locked in The Brig, and was banned from going on the mission for the next day. At the last minute, however, Rolf Emerson ordered the release of Bowie for the mission, much to the annoy of Dana. (Masters Saga: "Prelude to Battle")