The sum total of all knowledge in the Federation. Well that is the idea at least. The truth comes slightly close. Anything that has ever gotten into computer databases Federation wide is part of the database. From facts about supernovas to Romulan recipes.
All this accumulated knowledge is managed by the super descendant of Google.and wiki software. Appended to that are personal agents, education agents and other secondary expert systems. It is open and available to any member of the Federation that can access a PADD.
Some people (nervously) believe that the Database itself has achieved sentience. Several researchers have poked the database trying to prove or disprove this theory. What can be said is that plenty of sentient systems are part of the overall Federation datanet. That could well be enough to make the database itself look to have a mind of its own.
Conversation with said sentient computers indicates they do not believe the database itself is sentient. It is after all, just data. The various and sundry access and expert agents, including themselves can make it look that way. If the organization system of the database has itself achieved sentience it has not told them.