The short answer ( but slightly longer than Berny's ):
They take input from sound sources (tv, dvd player, iPod, etc.), amplify it, and output it to other devices (dvd burners, vcrs, etc.) and to speakers.
Most amplifiers also are capable of processing the input in some way. They can be set up to alter the sound (e.g. enhance the bass), modify the number of channels (e.g. convert from stereo to mono), or decode encrypted data into a format usable by the output devices.
If you really want to see first hand what an amp does, take an iPod or walkman to a store and use a minijack to RCA cable to plug it to an amp. Then press play. You'll notice that your tiny little iPod or walkman can now pump out massive amounts of sound to the speakers and that, by using the equalizers, you can modify how that audio sounds or what other devices receive that audio.
If you want a longer more technical answer, just let me know.
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