In the early days of computing, computer memory was made of wires passing through tiny doughnut-shaped magnetic rings called cores. Hence the term "core" means memory. A dump is to transfer the content of the memory verbatim to record the state of the computer. In early days, a dump was actually a stack of computer printout a few hundred pages long containing all hexadecimal numbers. Programmers read these reports to investigate the cause of a crash.
The term is sometimes used on Usenet for a posting that describes what has been happening in the poster's life, especially if it involves emotional stress; the implication is that the material has not been edited or analyzed.