Data crystals were small, sophisticated information storage devices able to store large amounts of information. They could be connected to dataports.
In the 2250s of the mirror universe, the Terran Empire rebellion used data crystals to store information on their listening posts. In 2257, Shukar gave the ISS Shenzhou's Captain Michael Burnham, who was posing as her Terran counterpart, was given a data crystal that contained the location of the Rebellion's listening post. (DIS: "The Wolf Inside")
Prior to Arissa's undercover assignment to the Orion Syndicate, which required her memories to be altered, a copy of her memories were stored inside a data crystal so that her identity could be restored after the assignment was complete. (DS9: "A Simple Investigation")