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When a clock speed number is quoted for a computer it applies to all cores on the processor. A core is an individual processing unit on the CPU. Each core can process data on its own. In a way, having a processor with two cores is like having a computer with two processors, although this is a generalization.
Adding cores to a processor does not result in a linear performance increase of Intel CPU processor speed. For example, let's say you have a single-core 2Ghz processor and a dual-core 2Ghz processor. The dual-core processor does not function like a 4Ghz single-core processor.
However, the extra core does mean it is possible to process two threads of data at once. This makes it easier for the processor to handle multi-tasking, and there are some programs, like video editing software, that dramatically benefit from the addition of cores.
Dual cores are the industry standard today. Single-core processors are only found in some low-power laptops. Quad core processors are becoming more common, but aren't necessary for the average user. You only need a quad-core if you do 3D rendering or video editing.