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

Answer: 
Like most terms, it depends on context.

* The term **cpu core** is frequently used these days. It refers to one of the independent processing units of [a multi-core processor](http://en.wikipedia.org/wiki/Multi-core_processor).
* The term **core memory** is a leftover from an early form of random access memory (RAM). [Magnetic core memory](http://en.wikipedia.org/wiki/Magnetic_core_memory) was first patented in 1947 and was used in early computers through the 50s and 60s. According to Wikipedia's article, magnetic core memory was replaced by integrated silicon RAM chips in the 1970's. Unlike modern silicon RAM, core memory was non-volatile -- it retained its contents indefinitely without power.
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.