Battlestar Galactica uses quite a bit of our own military terminology, as well as its own special lexicon.
Action Stations - an alert status. In the Colonial Fleet, there appears to be three. "Condition One," "Condition Two," and "Condition Three." Similar to a "red alert," "condition one" is the worst action station to be at, as it means you're about to be attacked.
Ambrosia - booze. Typically green, and potent. Most likely similar to Absinthe.
BSG - stands for both the name of the show and "BattleStar Group." Galactica's insignia is BSG 75, for instance. Typically a battlestar doesn't float around on its own, it has system of smaller support ships, like gun ships, medical ships, supply ships, etc.
CAG - stands for "Commander, Air Group". Basically, the CAG is the head viper pilot. In the Navy, a GAG would typically be of equal rank to the ship commander, but in the Colonial fleet, the CAG appears to be lower ranking than, say, Tigh. Or at least Tigh makes it seem that way.
CAP - stands for "Combat Air Patrol." Typically this is like a guard post, consisting of two or more Vipers, that fly around the Fleet at all times.
CIC - stands for "Combat Information Center." On a battlestar, this could be considered the "bridge," as it contains both the helm, communications, and computerized weaponry/navigation controls.
DRADIS - stands for "Direction, RAnge, and DIStance." It's basically radar in space. A DRADIS contact is anything that shows up on the DRADIS, whether that be enemy or friendly ships, or a planet.
FTL - stands for "Faster Than Light." It is a secondary propulsion system aboard military vessels, and a handful of civilian vessels, that allows the ship to "jump" long distances.
Nugget - a pilot trainee. Same as the American term. (If you pass training, you become a rookie. Or a "rook," as they say.)
Pyramid - the "national sport" of the Colonies, similar to basketball, though there appears to be three hoops. (In the shape of a triangle.) On the original series, the game was called "Triad."
Sit-rep - stands for "Situation Report." Generally this term is screamed a lot, as mostly disoriented leaders try to get a handle on what's going on.
Tylium - the type of fuel the Fleet uses in its ships. Nearest I can figure, it's organic, and needs to be refined in order to have the properties necessary to run a spacecraft.
XO - stands for "Executive Officer," typically second in command. Performs more of the managerial duties aboard a battlestar. Though, I don't see Tigh as the spreadsheet sort of guy.