The chambering, or the chambering of a firearm, is referring to the design of the chamber, which is located inside the barrel of the firearm typically, certainly for rifles and shotguns. It refers to the physical dimensions of that chamber and the amount of pressure it is designed to withstand during discharge. It determines the kind of ammunition that can be used in the firearm.
For example, the .308 Winchester calibre rifle that we spoke of earlier would have a chamber that is designed and manufactured for discharging .308 Winchester calibre ammunition. The barrel has a chamber, but the calibre of the ammunition that it uses is referred to as the “chambering”, or “chambered for” or “chambered in”. There are a variety of variations on how the language is used.