From ReloaderFred...

"Any "ring" around a cartridge case is called a cannelure. It can have several different purposes. The original purpose was to prevent a bullet from seating further into the case (bullet setback) in autoloading pistols and revolvers. A second cannelure higher up was to help with bullets pulling out under recoil in revolvers. These days it's also used to identify different brands and types of ammunition.

In the late 1800's and early 1900's, ammunition could be handled roughly and carried in saddlebags for an extended period of time. The bullets were pretty much pure lead and soft, with a BHN of around 5 or 6. Neck tension and crimp weren't always successful in holding the bullet in place, so cannelures were added.

I've seen cannelures within 1/8" of the case mouth on S&B .38 Special, and within 1/8" of the case rim on MagTech .38 Special. I've also seen cannelures used on military 5.56 cases near the base of the case to indicate blank ammunition, etc.

A cannelure can have many uses, both practical and cosmetic.