In small arms, caliber (American English) or calibre (British English) is the distance measured between the 'lands' in a rifled barrel, measured in inches (US/UK) or mm (continental Europe). It is often informally used as a description of the type of arm (e.g., .45 caliber pistol, 9mm ditto) or cartridge.
Note that caliber is only a very rough approximation of the power of a cartridge. Other variables that come into play include bullet weight & shape, powder capacity of the cartridge casing, and peak operating pressures.
In large naval guns (cannons), caliber refers to the length of the barrel, expressed as a multiple of the bore diameter. So the great guns of the Iowa class battleships are properly referred to as 16"/50 caliber as they have a 16 inch diameter bore and are 800 inches (approx 20 meters) long.