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

Answer: 
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.
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.