EEPROMS (Electrically Erasable Programmable Read-Only Memory) are a type of non-volatile memory (they maintain the info even when not powered. You can read more about EEPROMS on Wikipedia.
They are used by Pi HATS (Hardware Attached on Top) EEPROM. Per the Raspberry Pi Foundation's blog.
The EEPROM holds the board manufacturer information, GPIO setup and a thing called a ‘device tree‘ fragment – basically a description of the attached hardware that allows Linux to automatically load the required drivers.
They should not be used for anything but communicating with the HAT's EEPROM.
The blog post announcing HATs can be found here, and the HAT spec can be found here.