(covers information from several alternate timelines)
The Federation database was a database of the United Federation of Planets.
In the 2260s of the alternate reality, information on escort vessels, frigates, cruisers, scout ships, science vessels, survey ships, transport ships, hospital ships, supply ships, mining vessels, carriers, corvettes, diplomatic vessels, support vessels, as well as Starfleet Academy, Starfleet Medical, Starfleet Corps of Engineers, Starfleet Intelligence, Starfleet Operations, Starfleet Tactical, Starfleet Security, Starfleet Administration, Starfleet Science, Starfleet Research, Starfleet Diplomatic Corps, Starfleet Communications, and the M-class planet Altamid were located in the Federation database. (Star Trek Beyond)
Also available in the Federation database were inventory logs and maintenance logs. (Star Trek Beyond)
According to a graphic created for Starbase Yorktown, the Federation database had 756 references to the planet Cygnus VII. [1]
As early as the mid-23rd century, the Federation database listed lifeforms and species such as the Zaldans and Zan Periculi. The DNA of the latter was among the species tested for compatibility with tardigrade DNA by Paul Stamets, but it proved incompatible. The Daystrom Institute classified database housed potentially more information on lifeforms than the Federation database. (DIS: "Choose Your Pain")
Before the founding of the Federation, the Interspecies database offered the same information.
In 2371, Benjamin Sisko suggested the use of the Federation database to Jadzia Dax to find a match of the stranger and the music she remembered several times. (DS9: "Equilibrium")
In 2374, Captain Kathryn Janeway found a single entry about Annika Hansen in the records of Deep Space 4 after some digging through the Federation database. (VOY: "The Gift")
Janeway later advised Seven of Nine to use the Federation database if she want to know more about her parents, Magnus and Erin Hansen. (VOY: "The Raven")
In 2375, Seven of Nine assumed that Species 8472 had access to a Federation database when the crew of the USS Voyager discovered a replicated Starfleet Academy and Starfleet Headquarters in San Francisco aboard Terrasphere 8 in the Delta Quadrant. Captain Kathryn Janeway later told "Boothby" to check their Federation database to learn that Janeway told the truth when she claimed that the Federation had no knowledge about the realm of Species 8472. (VOY: "In the Flesh")
According to the Federation database, a graviton ellipse travels through subspace, emerging occasionally without warning. Ellipses have only been observed a handful of times. (VOY: "One Small Step")
When Seven of Nine told Commander Chakotay about a possible conspiracy, she mentions that according to the Federation database, the Maquis were victims of several unauthorized Starfleet missions. (VOY: "The Voyager Conspiracy")
In 3189, when Commander Michael Burnham was researching The Burn in Federation databases, she flagged the experimental program SB-19. (DIS: "Unification III")