Thermal Grease (also known as thermal paste, thermal compound, and thermal interface material) is a substance designed as a heat conductor for use in electronics. Processors (both central [CPU] and graphics [GPU]) are in greatest need of this substance, since they generally produce the most heat of all common electronic components.
To help dissipate a processor's heat, it usually will have a heat sink, which is usually a metal object with fins or pins extending out into the air to heat the air and cool the heat sink. When one piece of metal is pressed firmly against another, heat can exchange fairly easily. However, imperfections in the two surfaces reduce the transfer rate. Heat can be transferred across such gaps, but not in an efficient manner, since air has an extremely low thermal conductivity. For this reason, a filler substance is used in between these two surfaces. There are multiple kinds of filler material, but thermal grease is perhaps the most common type.
There are three main bases for this thermal transfer compound: metal (including Silver), ceramic, and carbon. However, there are more differences that the base alone. Different compounds are formulated with each base, with the general goal of decreasing the insulative properties to that heat is transferred better. Where possible, electrical conductivity is generally avoided to prevent mishaps, as well.
When Computers are manufactured, some transfer medium is inserted between the Central Processing Unit and the heat sink. It is usually thermal grease, but not always. However, if someone is assembling their own computer, they will need to add it. There are times when people need to add it for other reasons. If they are replacing their processor, it will probably be necessary to add some more if this is what was originally used. Sometimes the thermal grease will also dry out. Although somewhat effective still, some people choose to clean off the old and add new. Replacing this grease is also advisable if it dries out, and the processor and heat sink are separated. Since it is no longer a semi-liquid, it will not properly fill the microscopic gaps it is intended to.