The old world used them to record large amounts of data, most of the data have been corrupted, but the Research Center might be able to get something useful out of it.
Data Discs can most commonly be found by mining in Abandoned Ruins. They cannot be tracked through the relic scanner, but may sometimes be bundled inside boxes with other relics. They can also occasionally be found by breaking wooden crates in the Hazardous Ruins and in Amber Island's Cave.
The player may also receive some Data Discs in the mail as a monthly Workshop Ranking reward.
They are also used by the Recovery Machine in the Research Center to form Relics out of Relic Pieces. However, the Recovery Machine reward from donating 10 items to the Portia Museum does not consume discs.
Data taken from game assets, game version 1.0. Listed values are without The Giver skill, which gives an extra 1-2 points.
All other characters will default to Neutral (+1).