A database was a repository of knowledge.
The biggest database in N-Space was a title held by the Dalek Pathweb, which was even bigger than the Matrix. (TV: Twice Upon a Time [+]Steven Moffat, Doctor Who Christmas Special 2017 (BBC One, 2017).)
TARDISes had a database known as a TARDIS Information system. (TV: Castrovalva [+]Christopher H. Bidmead, Doctor Who season 19 (BBC1, 1982).)
By 2007, the Torchwood files covered numerous old databases, compiling a detailed profile of the Doctor. (TV: Love & Monsters [+]Russell T Davies, Doctor Who series 2 (BBC One, 2006).)
Apologising for not being able to find any information about Ruby Sunday's family, Davina McCall told her that if her parents weren't on some kind of database, then she and her people couldn't find them. (TV: The Church on Ruby Road [+]Russell T Davies, Doctor Who Christmas Special 2023 (BBC One and Disney+, 2023).)
In 2046, Roger ap Gwilliam made DNA testing mandatory for all UK citizens, creating a DNA database from it. Although Ruby's parents weren't in the databases Davina's people had searched, the Doctor and Ruby realised that they would have to be in Roger's database if they were both still alive in 2046. A search of the database identified Ruby's parents as Louise Miller and William Benjamin Garnet. (TV: Empire of Death [+]Russell T Davies, Doctor Who series 14 (BBC One and Disney+, 2024).)