EEPROM is a handy, non-volatile storage space that works well for storing data such as calibration or tuning constants that are not practical to hard-code into Flash.
It is unusual to run out of EEPROM. And it is not often practical to use EEPROM to offload SRAM data. But we'll mention it here for completeness. Using EEPROM requires that you include the EEPROM library.
The EEPROM library gives us 2 functions:
Read a byte from the specified EEPROM address
void write(int, uint8_t)
Write a byte to the specified EEPROM address
Note that while reads are unlimited, there are a finite number of write cycles (typically about 100,000).