It is EEPROM,that is,by applying a voltage you can read/write in it.Now,depending upon the technology used to manufacture the EEPROM,there is a limit on how much times you can perform read/write operations in it before it loses the capacity to store memory.
In ROM,once you burn it,it is fixed.Permanent.You cannot change it.
Do not know what 'AVR' device you are referring to but typical AVR or PIC micros have a EEPROM at least 100,000 r/w cycles
AVR EEPROM chips seem to have about 1,000,000 r/w cycles.
To understand the different types of micro memory these links might help you.. there are many others on the web that explain things in more detail if you search. http://www.avr-tutorials.com/general/avr-memory-map **broken link removed**