Core Memory is the memory and data storage system of the machine-like Aparoids. While it's quite possible that every individual Aparoid has a core memory, presumably only exceptionally strong Aparoids capable of warping through space contain information such as the location of the Aparoid Homeworld which is vital to an attack by the forces of the Lylat System. Since the core memory is, of course, housed within the body of the Aparoid, destroying or incapacitating the the creature can easily damage it, as was the case with the core memory recovered from a flying Aparoid on Fortuna. The Star Fox Team was able to recover a complete specimen from an Aparoid which attacked the Katina outpost, but it was stolen Pigma Dengar, who believed he could become rich from its sale. Pigma was pursued and eventually tracked to the Meteo asteroid field, where he was defeated in a battle and presumably destroyed, and the core memory was recovered for research.
In real life, "magnetic core memory," sometimes simply called "core memory," is an early form of computer memory which stores information using the magnetic polarity of wires threaded through magnetic ceramic rings, called the "cores." Although the technology was outmoded by silicon chips in the 1970's, modern computer memory is sometimes still referred to as core memory.