To store data so that it available after a reset or powering off the Arduino you need to write it to non volatile memory. This means either using the limited amount of EEPROM built into the Arduino or an SD card, which can hold much more. Using EEPROM does not require any extra hardware but each byte of such memory can only be written to a fixed number of times before you might begin to see problems.
How much data do you need to store and how often is it likely to change ?