The heat sink is a highly conductive metal; normally composed of copper or the cheaper alternative; aluminium, what this effectively does it increase the surface area of the component to speed up transition to the air. The air movement from the fan then helps to force convection and move the air even faster! So having a fanless pc means losing a lot of the computer's ability to transfer heat from vital areas into the atmosphere.
So why would you want to build a computer without any fans you ask? Well there are several reasons. One is noise; fans tend to make a fair amount of noise, the faster they go the more noise they produce, though there are silent fans, which produce very little noise, as well as things which can be done to reduce the noise of other fans, such as rubber mounting brackets which reduce vibrations to the case. Other options for reducing noise include putting the computer in an enclosure.
Noise isn't the only reason however; one of the big drawbacks of having a computer system which relies on airflow is dust. Dust builds up in just about any computer system over time and will vastly reduce the effectiveness of heat sinks as it clogs them up effectively insulating their surface. It can also clog up fans, inhibiting air flow and reducing the effect of fans though how fast dust builds up is largely based on the environment on which it resides. Typically dust isn't too much of an issue, since you can just clean it out every so often in the case of home PCs.
On the other hand in some industrial environments there can be huge amounts of dust to clog a system up and it may not be viable to keep cleaning out the computers or to even risk damage to components. This can become especially important for environments which may have fine metal powder which could short circuit a computer and even potentially cause a fire. In these cases the only real option is to have the computer dust proof and sealed off which makes fanless computers essential.
Such computer work in such a way that the whole case becomes one big heat sink, often sporting extruded aluminium designs to increase the surface area. Obviously however, such systems will not be as effective as fanned computers at ditching heat into the atmosphere, so on top of their designs, most computers which rely on passive cooling also have to minimise the amount of power they use; your 200W CPU's simply won't last in this kind of case. That can be another benefit however, lower powered computers, obviously, use less power, which means running costs associated with them are lower as well, making them ideal for use in business and industry.
So next time you're in the market for a computer, consider going fanless! It's quieter, lower maintenance and cheaper to run!