The War College was a Colonial Fleet military educational institute that likely taught its officers many tactics and other subjects pertaining to military logistics in battle.
Lee Adama knows of a technique from War College using electric pulse generators to create an EMP burst as a means of fending off the Cylons and incapacitating any warheads. Using generators on Colonial One that were offloaded from Galactica (presumably as part of her decommissioning), Lee Adama successfully uses this method to disable two nuclear missiles that the Cylons fire at Colonial One.
The pulse mimics a nuclear detonation and blinds the Cylon DRADIS, making the attack appear successful. According to Adama after the ruse, in computer simulations in War College, the Cylons never fell for the trick (TRS: "Miniseries").
Kara Thrace did not attend War College, according to Saul Tigh's comments (TRS: "The Hand of God").
Notes
- In real life, most "War Colleges" teach experienced, high-ranking military officers. For example, the U.S. Army War College's average age of students is 45 years and the typical rank is lieutenant colonel.