The purpose of the "belt" on belted cases (often referred to as belted magnums) is to provide headspacing; the extractor groove is cut into the belt just as it is cut into the case head on a rimless case. The belt acts as a rim on what is essentially a rimless case. The design originated in England with the .375 H&H Magnum. The addition of the belt allowed the cartridge to properly headspace, despite the relative lack of a definite shoulder. The reason for the lack of a definitive shoulder was that these old British cartridge cases were intended for firing cordite charges instead of modern smokeless powder. Cordite was extruded as spaghetti-like rods, so the cartridge cases had to be fairly cylindrical shaped to accommodate the cordite propellant rods. The belt was carried through on other cartridges derived from the .375 H&H, in some cases to prevent the higher-pressure magnum cartridge from accidentally being chambered in a gun with a chamber of similar size.
In the USA, the belt became somewhat synonymous with "magnum" during the late 20th century. More recently, new "magnum" cartridges introduced in the USA have been rimless or used rebated rims based on the .404 Jeffery that fit the same .512" bolt face used for the belted cases.