What does thermal paste do?

It allows for an efficient transfer of heat from the IHS of the processor to the base plate or water block of the CPU cooler that is designed to dissipate that heat.

What else is thermal paste used for?

Thermal paste is used to improve the heat coupling between different components. A common application is to drain away waste heat generated by electrical resistance in semiconductor devices including power transistors, CPUs, GPUs, and LED COBs.