Terry Burrell is an officer in the Colonial Fleet Marine Corps.
He is on board Cloud 9 on leave when Sesha Abinell and her group take their hostages. He's also part of a failed rescue attempt which results in him getting shot in the leg, two dead Marines, and one dead hostage-taker (Sacrifice).
Notes
There is some confusion over his rank. Starbuck refers to him as 'Gunny', suggesting he is a Gunnery Sergeant, but the closing credits of Sacrifice list him as 'Lt. Terry Burrell', which makes the 'Gunny' comment very confusing. At this time, we should consider him a Lieutenant, since that's the rank the credits list him as, with the 'Gunny' comment being a reference to a recent promotion from Gunnery Sergeant to lieutenant.