What are some larger cartridges belted? What is the purpose of the belt in a belted magnum cartridge?

There are a couple of easy answers here, with the most important one being that the belt offers tangible head-spacing benefits to the cartridge. 

The head-spacing is reliant on the belt, which allows for the sometimes awkward profiles of some of these cartridges to still be precisely and safely shot in the rifle. 

The belt also can help with allowing for some expansion in the chamber which can mitigate pressure and heat concerns in some of the larger magnums.

Additionally, there is some credence to the idea that the belted cartridges are more flexible and easily reused thanks to the additional durability of the added belt. 

Most of this comes from a period in the 1950’s that saw the H&H Magnums rise to prominence. The use of the .300 H&H and .375 H&H magnums as wildcat cases, and for use in other magnum cartridges, presented a perfect storm for the belt to become part of the magnum landscape. This is because those cartridges used a belted configuration for the brass, and were made to a high standard. They (Holland & Holland) initially used the belt for, you guessed it, a head-spacing component, because the shoulder angle and tapered casing made precision head-spacing, and therefore safety and pressure concerns a necessary component of the cartridge and rifle equation.