A Core 2 Duo prcoessor has 2 cores. (basically 2 processors) A Core 2 Quad has 4 cores (basically 4 processors)
Clock speeds are not multiplied by the number of cores either, that is a misconception.
As of yet there are few games that require a quad core for good framerates, however professional applications will perform better with quad cores and lots of RAM.
A dual core is preferable for everday computer use like internet browsing and microsoft office stuff.