All modern PC CPUs produce enough heat that they need a heat sink. Almost all of them need a heat sink with a fan. Many heat sinks come with some sort of thermal transfer thingy pre-applied - a patch of grease, or a square of chewing-gum-like semi-solid material, or just a rubbery pad for the low performance units. Most CPUs don't produce enough heat that the stuff you put between the chip package and the heat sink matters very much, as long as the computer case has decent ventilation and the ambient temperature isn't sauna-like. There just has to be something between CPU and heat sink.
The reason why there has to be something there is that the two mating surfaces of processor and sink aren't flat. They may look flat. They may have a mirror polish. But, on the microscopic scale, they look like a scale model of the Andes. And the mountains on one item do not match the valleys on the other.
Without thermal transfer compound, everywhere heat sink metal doesn't mate with CPU package material is a teeny-tiny air gap. Air is a good thermal insulator. As long as your heat sink looks flat when you lay a ruler on it then there'll be a decent amount of actual contact, of course, but the amount of heat that'll actually make it around the air gaps may be surprisingly small.
Hence, thermal compound. It's grease with lots of minuscule thermally conductive particles mixed into it, basically. It doesn't conduct heat as well as direct contact, but it's a heck of a lot better than air gaps.
Bear in mind that we're talking about something we're using as a THIN barrier that, unless you're into the insane OCing shenan