The central processing unit, or CPU, is the chip (or group of chips) that does the actual processing in the computer. On your computer (and mine) the CPU is a single chip called a microprocessor. There are many different types of microprocessors in use today on servers, desktops and notebooks. All of them perform the same basic processes in approximately the same way. The CPU is composed of an arithmetic and logic unit, or ALU, and a control unit. The ALU does the actual computing and the control unit tells the ALU what to do. In a microprocessor both of these are on the same chip.
The CPU executes instructions (which are individual components of computer programs). In order for the processor to execute these instructions they have to be in a form called machine language, a binary code (see various links under data). Different types of processors use different machine languages. Most current personal computers have processors with multiple cores. Multi-Core processors essentially have two separate processors on the same chip, which gives them the capability of executing separate threads simultaneously (as long as the operating system and application were designed with this in mind).
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Wikipedia Central Processing Unit
Wikipedia Microprocessor
Wikipedia Multi-Core