A linguistic database was a compiled collection of known languages.
The Vulcans maintained such a database as early as 2151, when they shared samples of Klingonese with the United Earth Starfleet. (ENT: "Broken Bow") The Enterprise later maintained its own database, which could be tied in with the universal translator. (ENT: "Fight or Flight")
When Hoshi Sato suffered from hallucinations while in a pattern buffer, she claimed that crewman Baird had translated a complex language, even though he knew nothing about the ship's linguistic database. (ENT: "Vanishing Point")
In 2161, shortly before returning to Earth to decommission Enterprise, Ensign Hoshi Sato figured she would need a week to purge the linguistic database. (ENT: "These Are the Voyages...")
In an attempt to communicate with the Tamarians in 2368, Deanna Troi searched several linguistic databases for the term Darmok. (TNG: "Darmok")
In 2374, Arturis was given access to USS Voyager's linguistic database, from which he learned Klingonese. (VOY: "Hope and Fear")
In 2375, Seven of Nine activated One's linguistic database, so he could begin assimilating information. (VOY: "Drone")