A rim is an external flange

Flange

A flange is an external or internal ridge, or rim , for strength, as the flange of an iron beam such as an I-beam or a T-beam; or for attachment to another object, as the flange on the end of a pipe, steam cylinder, etc., or on the lens mount of a camera; or for a flange of a rail car or tram wheel...

 that is machined, cast, molded, stamped or pressed around the bottom of a firearm

Firearm

A firearm is a weapon that launches one, or many, projectile at high velocity through confined burning of a propellant. This subsonic burning process is technically known as deflagration, as opposed to supersonic combustion known as a detonation. In older firearms, the propellant was typically...

s cartridge

Cartridge (firearms)

A cartridge, also called a round, packages the bullet, gunpowder and primer into a single metallic case precisely made to fit the firing chamber of a firearm. The primer is a small charge of impact-sensitive chemical that may be located at the center of the case head or at its rim . Electrically...

. The rim may serve a number of purposes, the most common being as the place for the extractor

Extractor (firearms)

An extractor is a part in a firearm that serves to remove brass cases of fired ammunition after the ammunition has been fired. When the gun's action cycles, the extractor lifts or removes the spent brass casing from the firing chamber.-Overview:...

 to engage. Nearly all modern ammunition

Ammunition

Ammunition is a generic term derived from the French language la munition which embraced all material used for war , but which in time came to refer specifically to gunpowder and artillery. The collective term for all types of ammunition is munitions...

 has some type of rim, the major exception being caseless ammunition

Caseless ammunition

Caseless ammunition is a type of small arms ammunition that eliminates the cartridge case that typically holds the primer, propellant, and projectile together as a unit...

.
There are various types of firearms rims in use in modern ammunition. These types are rimmed, rimless, semi-rimmed, rebated rim, and belted.