Carburetor heat - usually referred to as carb heat - does what it says on the tin. It is a system in light carburetted piston engines, these days usually in light aircraft but also in older automobiles, which directs hot air through the carburetor to prevent or remove icing in the carburetor itself.
Ice can form in a carb when the intake air is has moisture in it, even if the ambient temperature is quite far above the freezing point. This is because at certain power settings, air passing through the carb will undergo significant cooling for two reasons, and those two cooling influences can drive the temperature low enough to cause ice crystals to form and collect.
First, at lower throttle settings, the air entering the carburetor isn't moving that quickly, and engine vacuum will be at a high differential to the outside air. As the air enters the carb, it will enter an extremely low pressure area and as a consequence the pressure will drop. In addition, as it passes through the venturi, it will speed up significantly. This, in turn, will cause another pressure drop. These pressure changes will cool the air as it expands.
Second, as the air passes through the venturi, fuel will be vaporized into the airstream. The fuel, as it evaporates, will pull the heat of evaporation out of the surrounding air. This is why pouring room-temperature rubbing alcohol on your hand will make it feel cold - as the alcohol evaporates quickly, the heat of evaporation is removed from your hand and the air around it.
These two effects, together, can make carb icing a problem even on quite warm days - in fact, it is generally a worse problem on warm days, because warm air can contain far more moisture than cold air. Although it's bad enough if this happens in an auto engine, it can be extremely dangerous if it occurs in an aircraft engine.
To cope with this problem, the pilot or driver will usually have access to carb heat. When activated, the carb heat system will open a valve in the air intake which draws air across a heat exchanger usually connected to the exhaust manifold of the engine. Hot air will flow into the carb, melting the ice. The drawback of carb heat (and the reason it isn't left on all the time) is that the hot air is lower density, which means it contains less oxygen - so when carb heat is on, the engine will noticeably lose power, typically a few tens or hundreds of RPM.
In light aircraft with carburetted engines, checklists usually instruct the pilot to add carb heat whenever reducing power or within designated ranges of temperature deemed as high risk. If you are flying a light aircraft and your engine suddenly begins to run rough and/or lose power, the first thing you should do is add carb heat!