EEPROM stands for Electronically Erasable Read-Only Memory. A non-volatile memory that will retain information when power is off. It is typically used for data that changes rarely like device parameters, etc. The AVR's internal EEPROM is accessed via special registers, which control the address and the data to be read or written and control flags.
Standard C does not have a model of how to access such memories, so every compiler is unique. This Tutorial explains how it can be done using AVR GCC.