A field gun is an artillery

Artillery

Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the range of effect of personal weapons...

 piece. Originally the term referred to smaller gun

Gun

A gun is a muzzle or breech-loaded projectile-firing weapon. There are various definitions depending on the nation and branch of service. A "gun" may be distinguished from other firearms in being a crew-served weapon such as a howitzer or mortar, as opposed to a small arm like a rifle or pistol,...

s that could accompany a field army on the march and when in combat could be moved about the battlefield in response to changing circumstances, as to opposed guns installed in a fort, or to siege cannon or mortars which were too large to be moved quickly, and would be used only in a prolonged siege

Siege

A siege is a military blockade of a city or fortress with the intent of conquering by attrition or assault. The term derives from sedere, Latin for "to sit". Generally speaking, siege warfare is a form of constant, low intensity conflict characterized by one party holding a strong, static...

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Perhaps the most famous use of the field gun in terms of advanced tactics was Napoleon's use of very large wheels on the guns that allowed them to be moved quickly even during a battle.