The Brig is a temporary holding cell in Terra Nova. It is where hostages and prisoners are kept. There is an alarm system used for torture. The cell is most notably seen as having red lighting all over the walls and pillars.
After Boylan was caught and arrested for being a suspect for being the Sixers' spy, he was thrown in the brig. ("Proof") Andrew Fickett, while thought to be the geologist Ken Horton, was probably thrown in the brig after he was unmasked and tried to kill Maddy Shannon.
Taylor demanded that Boylan confess to being the spy, however, Boylan wasn't and therefore wouldn't confess. Taylor then tortured him by playing a loud alarm. Boylan was left to sit in the brig. Taylor also tried to drug Boylan's food to get him to relax and confess. Boylan, in his drugged state, told Jim, thinking he was Taylor, that he was going to blackmail Taylor with the fact that he killed General Richard Philbrick. Jim was later thrown in the brig as Taylor didn't want him to tell the colony about Taylor being forced to kill a man. ("Vs.")
After the Phoenix Group took over Terra Nova, they threw anyone who resisted occupation in the brig. Lucas later had Jim and Josh thrown in there for fighting the guards. Josh was let go, but Jim was kept in there and tortured by Lucas. Weaver eventually helped Jim escape after he was threatened to be killed by a parasite by Elisabeth. ("Occupation-Resistance")