What is CPU thermal grease or paste?

The simple answer is thermal grease is to aid in the heat transfer from the cpu to the cooling fan. It is not like a lubricant that needs to be changed often. Usually when you buy a new oem fan and cpu there is paste already installed on most fans just remove the thin plastic protector before you install the fan. If you remove the fan for whatever reason you should change it then. Also there are better brands that transfer heat more than what is installed on your fan.