The most common mode of distorting a signal in an effects pedal is to "clip" the signal by means of a pair of diodes connected in parallel. When the threshold voltage of the diodes is exceeded, the signal above that magnitude is dumped, usually to ground. This is described in more detail in that Geofex article linked by Mainestratman.

Somewhere along the line, somebody got the idea that "Hey, LED's are just diodes that emit light--you should be able to use those for signal clipping, too!" And you can. But they have a very high voltage threshold (2V and up), so they don't clip as much signal as the traditionally used types (0.3 - 0.7V typically). Consequently, their output tends to be louder, less compressed, and less distorted overall.

This first showed up in "boutique" pedals, where some enterprising individuals figured out that you could substitute about 80 cents worth of LED's for 5 cents worth of other diodes, and then charge $200 bucks more than "regular" pedals, and some people would pay it. Google "Landgraff Dynamic Overdrive" if you don't believe me...