Core: This is the graphics processor (GPU). Think of it as a CPU that processes what you see on your screen. The core speed (measured in megahertz) is the clock speed that the GPU runs at.
There's much more to GPU performance than just its clock speed, but if I tried to explain this, I'd just confuse the hell out of you. Read the guide that Cleeve linked to; if you have any more questions, ask him (he's the expert).
Memory: The graphics memory (also called VRAM) holds textures. VRAM clock speed can be measured in megahertz or gigahertz. Once again, there's more to memory performance than just clock speed, but I'm not going to try and explain it.
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