A field gun is a field artillery piece. Originally the term referred to smaller guns that could accompany a field army on the march, that when in combat could be moved about the battlefield in response to changing circumstances (field artillery), as opposed to guns installed in a fort (garrison artillery or coastal artillery), or to siege cannons and mortars which are too large to be moved quickly, and would be used only in a prolonged siege.
Perhaps the most famous use of the field gun in terms of advanced tactics was Napoleon Bonaparte's use of very large wheels on the guns that allowed them to be moved quickly even during a battle. By moving the guns from point to point during a battle, enemy formations could be broken up to be handled by the infantry or cavalry wherever they were massing, dramatically increasing the overall effectiveness of the attack.