Abbreviated recursively as LAME, It's now an anachronism in that LAME now is a full Mpeg 1 Layer 3 encoder, though it wasn't always that way.
LAME began as a patch for the Fraunhofer MP3 demo source (dist10) and, as such, couldn't make any output on it's own which is why it's named what it's named. But later on in 2000 a full rewrite was finished and the LAME system contained all project-owned code and discard anything proprietary.
Though the LAME project maintains that LAME is an educational tool to be used for learning about MP3 encoding. Even still, LAME is probably one of the 5 most used MP3 encoders available with the added benefit of being free. LAME is also most frequently used with the gpsycho acoustical model shapping system for better sound dynamics.
Since LAME is under the GNU GPL, most people think it's for hackers only. However, many user-friendly packages now have pre-compiled binaries of LAME included (such as Exact Audio Copy), though you can still compile from source if you like.
LAME's audio quality is usually rated as on par with the Fraunhofer encoder quality, though with tuning it can go well above that. LAME is also, with use of gpsycho, one of the few encoders that support CBR, VBR and ABR encoding modes.
The LAME project's home is currently at http://lame.sourceforge.net/