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 seems to have two brigs. One with at least two small cells with bunks. There is also another brig with one larger cell with no commodities for high-security prisoners. In the episodes in which the brigs has made an appearance, there is usually always a Marine guard standing watch inside the room. In the high-sec brig, there are usually around four.

Notable chracters who have spent time in the brig are:

Season 1

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
Apollo -- mutiny in Kobol's Last Gleaming, Part II and appearing in Scattered. He is able to be let out of the brig when on duty.

Season 2

Boomer -- shooting a superior officer twice in Kobol's Last Gleaming, Part II and appearing in Scattered
Chief Tyrol -- under suspicion of conspiring with the Cylon Boomer in Resistance
Cally -- for discharging a firearm without permission in a crowded corridor in Resistance and appearing in The Farm