Game cartridges have two or more chips - one is the ROM chip that contains the game and isn't rewritable, one is eeprom/FLASH which stores the save files and is rewritable, the additional chips may be memory controllers or additional, game-specific hardware (very rare - memory controllers are embedded on the silicone of the memory chips nowadays, mapper chips are a thing of the past and none of the 3DS games uses game-specific hardware as of today). That's how cartridges work in general, not just on the 3DS. If you want a source for this basic knowledge, read some articles on wikipedia concerning cartridges. If you want a 3DS-specific source, read up on 3DS-brew.
