The AT24C256 EEPROM provides a small amount of permanent storage for the Arduino, but can be tricky to use. The Hobbytronics website has an excellent article explaining how to use this EEPROM.

Library for using the Atmels EEPROM AT24C32/AT24C64/AT24C128/AT24C256/AT24C512 in Arduino projects. - cxmmeg/eeprom-08-AT24Cx ...

Some microcontrollers like Arduino have very limited internal storage space, so an external EEPROM will be suitable for small amount of data storage or for extending the data storage capability of a ...