Triggers on a bass drum are simple. You hit the bass pedal, and the trigger will detect the hit and send it to a "brain" or a trigger module which then plays a sample of a bass drum over the PA. That's a very basic explanation of a bass drum trigger.
From what I remember, Deliverance at least was recorded with acoustic drums, and then when it was mixed, Andy Sneap mixed it so it's 50% acoustic drums and 50% samples coming through for a thicker sound.