In any electronic circuit, keeping the components cool is very important from the point of view of reliability. With a small increase in temperature, the reliability goes down exponentially. Most electronic components show a degradation in performance with increase in temperature. While many of the components can keep their cool all by themselves, some of the power-hungry components cannot do without heat-sinks to efficiently remove the heat within. This is what you call passive cooling. When the ambient temperature in the vicinity of the electronic component is high enough not to allow any appreciable heat transfer from the heat sink to the surrounding air, one has to go in for active methods of cooling. Using a Peltier - also known as a Thermo-Electric Cooler (TEC) - is one such method.
A Peltier, as shown in the above pictures, has two surfaces. On forcing a DC current through a Peltier, it removes heat from one surface and passes it on to the other. Quite obviously, the first surface becomes cold while the other becomes hot. I can now place my electronic component on the cold side and a large heat-sink on the hot-side so that I have a neat way to pump out heat from the component. And yes, a thermodynamics guy would call such a device a heat pump.
The underlying principle - known as the Peltier Effect - is elegantly illustrated in the animation below [source: www.peltier-info.com]
While Peltiers can do an important job for you inside a high-end PC, especially if you are an over-clocker, they can also provide good amusement value if you wanted to freeze a few drops of water in a few seconds! I tried it out one sunny day with a solar panel driving just over an ampere of current through a small Peltier element mounted on a heat-sink. (You could as well use a good DC supply to drive your Peltier. But it certainly is funkier to use solar energy to freeze water!) It is advisable to apply a small amount of thermal grease between the Peltier and the heat sink to get better thermal conductivity. After making the connections, initially water vapour condenses over the cold surface and then freezes within a few minutes, if not seconds. Using a fan, taking hot air away from the fins, I got even better results. Under laboratory conditions of 26 degree celsius, a cold side temperature of -7 degree celsius was achieved! And yes the heat sink became quite hot, say 40-45 degree celsius. As the heat sink becomes hotter, the achieveable cold side temperature also goes up. This is where a larger heat sink helps as it will take a very long time to become hot. One more interesting thing. If you see that all of a sudden all the ice melts, it is mostly due to a passing cloud shading your solar panel :-)
Paul Peng gives a very neat and descriptive account of his experience with Peltiers on this page. And here's a video demonstration of the Peltier Effect:
One could ask, why dont people use Peltiers in refrigerators. The answer is Peltiers are expensive and yet quite inefficient. Cycling a refrigerant through a compressor, a condenser, an expansion valve and an evaporator (Refrigeration Cycle) is a far cheaper and more efficient way to cool our food stuff. But when it comes to meeting the cooling requirements in a small area and in a highly reliable fashion, nothing beats the Peltiers. After all, Peltiers are completely solid state devices with no moving parts.