An MP3 decoder is a software program that converts MP3 to another format. However, when most people mention MP3 decoder, they are talking about a program to convert MP3 to WAV.
Since most CD players cannot play MP3 format, mp3 decoders are used to convert MP3 to WAV before burning the files to a CD. The resulting WAV files can be played on any CD player. Most MP3 files are probably downloaded from free sites or with file sharing devices and then converted to WAV for custom audio CD creation.
The difference between decoders is speed, ease of use, and quailty of the resulting file. In our MP3 Decoder section, you can find links to scientific tests on the quality of some of the decoders.