A full explanation in french can be read at http://www.locoduino.org/ecrire/?exec=article&action=redirect&type=article&id=139 .
Roughly, EEPROM is small memory area which have two problems : first, the basic functions emmbedded in the IDE to write/read data in this memory is very basic, and second, its lifetime could be short (relatively) if you always write the same cell of this memory. This library try to answers to these two issues.
As for many of my libaries, a '#define EEPROMEXTENT_DEBUG_MODE' can be unremarked to have some debug informations and new functions to understand bugs in your sketch.