So what exactly are Music Modules anyway? Well, they are a mixture of MIDI files and WAV files.

As you probably know, a WAV file is a pure audio recording of a sound. It can e.g. contain a song, a news report or an audio message from one of your friends.

Midi files only contain the notes, the time that the note will begin to play and the note length. A MIDI does not contain the sound of the instruments that it has to play - it uses an instrument library which is already built in your sound card. The library of your sound card contains a fixed number of instruments and their sounds.

Modules are a lot like MIDI files. However, they contain an independent instrument library. You can import a WAV sample - for instance, the sound of a piano - into a module. After this, you can specify which note should be played, the time when the piano sound must be played and the length of this note. The tracker can in this way adjust the sample's pitch/tone to make the desired note and with the help of loops (that you have to make yourself), it can maintain the piano sound as long as you want.
So basically you can make a music composition with (short) sounds of musical instruments by triggering, pitching and looping them. This way you can compose a whole music track with sounds of real instruments and still maintain a low file size! =)
Additional info can be found on the following ModPlug page.