1. The interior diameter of the bore of a gun barrel, usually measured in inches or millimeters.
A gun barrel with an interior diameter of .357 inches in diameter is technically .357 caliber. Caliber measures the diameter of the bullet and has nothing to do with length or weight of the actual bullet, although calibers have taken on broader meaning in casual conversation. If someone refers to a caliber of 9mm, then they are really talking about a 9mm Luger cartridge and all the assumptions that go with that.
2. A sinister plot by gun people to make things extra-confusing for new shooters.
For example, .38 caliber really means .357 inches in diameter and .380 caliber really means .355 inches in diameter. 9 millimeter also means .355 inches in diameter. To keep things plenty confusing, .40 caliber really does mean .40 inches in diameter. Same with .45 caliber - that means .45 inches. However, .44 caliber really means .430 inches. Of course, .32 ACP (caliber) really means .312 inches. .30 caliber rifle bullets are particularly easy. Some are .308 inches and others are .311 inches. Got it? See, isn’t this gun stuff easy?