Dilithium is rewarded to players through several means, but it's awarded as unrefined ore. The refining process is slow, with players having a soft limit of about 8000 refined dilithium a week (veteran and subscription players can refine slightly more). You can also trade it for the game's microtransaction currency on a live market. Once you have it, you can use it to buy new ships, rare crafting items, special gear, and certain Duty Officers. The full guide should answer any lingering questions you have about the currency, although it does not ask at any point if the players are down with dilithium.