The bullet or Bore diameter of the gun
In small arms (rifles and pistols), the caliber refers simply to the approximate diameter of either the projectile (bullet) or bore (the hole in the barrel the bullet travels through).
In Naval rifles (they’re commonly called “guns” or “cannons” but the official term is “rifles”), the caliber is actually a ratio of the the length of the barrel divided by bore diameter. For example, Iowa class World War II battleships had 16 inch bore, 50 caliber rifles. The barrel length was 50 times the bore diameter or 800 inches (roughly 66 1/2 feet) long.
Calibre is the British spelling.