Blue Air Training provide training for military CAS (close air support) JTAC (joint terminal attack controllers).
JTAC trainees use the Blue Air planes as clockwork mice.
Trainees come from various ground forces/units, army, marines etc.
There are a number of similar companies that provide military training services (ATAC provide air-air 'topgun' fighter training, naval anti-air training etc).
Using civilian contractors for this sort of training is cheaper and more flexible than using non-combat military units.