Question: I was wondering what "core" means? CPU or memory or both?

Answer: 
The word "core" has multiple meanings. These days, it's mostly used to refer to the [actual processing units](http://en.wikipedia.org/wiki/Multi-core) within the CPU (now that they tend to have more than one), but it used to be that "core" referred to the [amount of memory](http://en.wikipedia.org/wiki/Magnetic_core_memory), not processing units, in a machine. Hence the term "[core dump](http://en.wikipedia.org/wiki/Core_dump)," which refers to a readout of memory as of just before a crash.
A core is a processing unit. It may or may not have a number of caches (small quick memory) of its own, depending on the design of the chip. What most people consider 'the memory' (ie the main RAM) is not directly connected to the idea of a core.