Apparently a Colonial military educational institute, likely studying war tactics and other subjects pertaining to military application.
Lee Adama learned a technique using the pulse generators to create an EMP-type burst as a means of fending off the Cylons and incapacitating any warheads. (It would appear to an uneducated enemy that a nuclear warhead had detonated. In simuations, the Cylons never fell for the trick.) Lee Adama successfully used this method when the Cylons came across the Colonial One using the Galactica's extracted pulse geneators (Mini-Series). Kara Thrace apparently did not attend War College (The Hand of God).