The brig on a ship is basically the bottom of the ship or the bowels of a ship where there are jail cells inside the ships brig.
Prisoners are that commit crimes while on the ship while in the military are sent to the brig and are locked in a jail cell in the brig for the duration of the ride on the ship.
Then when they get to dry land the prisoners in the brig are then sent to a jail or prison on dry land to serve out a sentence or get convicted of something and then sent to prison.
The brig is just basically a jail in a basement but on a ship.
Cruise ships also have jail cells where they put passengers who committed crimes while on the cruise ship.