What is Thermal Paste?
Thermal paste is a conductive material used to allow better flow of heat between two or more objects. In the computer world, it is used on heat sinks that are connected to the CPU and the GPU. This helps the CPU and GPU stay cooler by taking some of the heat off of the processor units and spreading it out across the heat sinks, which then allow the fans to cool, without the thermal paste on your CPU, it would overheat and performance would be crippled, as well as potentially frying your CPU/GPU.
Different types of thermal paste
There are different types of thermal grease that can be used (silver, pads, ceramic, tape, carbon, metal etc), though; the difference in conductibility and quality means the list can easily be shortened down to only two.
Silver Vs Ceramic
Using very small metal particles, silver paste is generally considered number one for conductivity when it comes to computers and gets my vote. It should be noted, though, that through independent testing, results have shown certain kinds of ceramic thermal paste to be more effective that silver. Ceramic paste is also cheaper to purchase and is not electrically conductive, where as silver thermal paste can cost twice the price of ceramic and can potentiality cause damage to your system if applied incorrectly as it is a conductor of electricity.