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.
Some further read :

* <http://en.wikipedia.org/wiki/Multi-core>
* <http://en.wikipedia.org/wiki/Central_processing_unit>

From what I understand, one or more core are part of a processor (CPU).

Memory can refer to the cache (a small and faster type of memory) or the RAM. The RAM isn't part of the CPU.