When a double action gun is uncocked and loaded, it may be fired by pulling the trigger. The trigger usually travels a good ways in double action, and during its travel it is cocking the hammer (moving it backwards against spring tension). When the hammer reaches a point far enough back in its travel, it is released and allowed to fall, thus firing the gun.
Many DA guns may also be fired single action (SA), but some are double action only (DAO).
The "double" in double action means the trigger performs two functions: cocking, and then firing, the firearm.