The central hardware of a starship's main computer, holding its processors and memory, whose loss or corruption leaves the vessel close to helpless.
The computer core is the physical heart of a starship's computer, a multi-deck structure containing the processors and memory on which every other system depends. Navigation, life support, replicators and the holodecks all rely on it, so damage to it is among the most serious faults a ship can suffer.
In Evolution, Wesley Crusher's escaped nanites breed inside the Enterprise-D's core and begin feeding on its memory, causing failures across the ship until Data helps open talks with them. In the Voyager episode Concerning Flight, raiders use a transporter to steal equipment from the ship, including the main computer processor, and Janeway must track it down with the help of the holographic Leonardo da Vinci.
Later Starfleet designs replace part of the conventional circuitry with bio-neural gel packs.