A memory core was an information storage device.
The Tenth Doctor was accidentally trapped inside the TARDIS' memory core. (GAME: Eye of the TARDIS)
Clara Oswald was able to reactivate Rusty's memory banks in its cortex vault. (TV: Into the Dalek)
Whilst K9 was imprisoned by the Sporraxx, they tried to access his memory core. (COMIC: Short Circuit)