Brig

Meaning: Prison; detention centre.

Brig is a US military term with one of two uses:

A jail or prison on board a U.S. Navy or Coast Guard vessel.
A jail or guardhouse, especially on the premises of a U.S. military installation.

The Galactica's brig seems to have one medium-sized cell with a bunk. In the episodes in which the brig has made an appearance, there is usually always a Marine guard standing watch inside the room.

Notable chracters who have spent time in the brig are:

Starbuck -- Striking a superior officer in the Mini-series
Aaron Doral -- Under suspiscion for being a Cylon agent in the Mini-series
Specialist Socinus -- Lying under oath and leaving a post in Litmus and is released in a deleted scene in Kobol's Last Gleaming, Part I
Gaius Baltar -- Act of treason by collaborating with the Cylons in Six Degrees of Separation
President Laura Roslin -- consequence of a successful coup d'etat led by Commander Adama in Kobol's Last Gleaming, Part II