Silicon heat transfer compound (thermoconductive paste) is a silicon-based paste used to lower the thermal resistance between a semiconductor and a heatsink. Since the surface of the semiconductor and the heatsink are not completely smooth there will always be some air between them. This air acts as a heat insulator, and increase the thermal resistance. By applying the compound these holes gets filled in, thus lowering the resistance.

A little story:

A few weeks ago, I was repairing a PC at the place I work. Anyway, two others work at the same office as me. They are university-educated programmers. One of them picks up a processor, and starts to play with it. He takes of the heatsink and turns to the other one:

Programmer 1: What's this?
Programmer 2: I don't know.

Then in a flash of enlightenment the first one finds out what it is: Correction fluid!.

I laughed until I fell of the chair.