I was wondering what "core" means? CPU or memory or both?
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.
The term core memory is a leftover from an early form of random access memory (RAM). 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.
The word "core" has multiple meanings. These days, it's mostly used to refer to the actual processing units 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, not processing units, in a machine. Hence the term "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.
Some further read :
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.