The processor is the part of the computer that actually does the computations. This is sometimes called an MPU (for main processor unit) or CPU (for central processing unit or central processor unit).
A processor typically contains an arithmetic/logic unit (ALU), control unit (including processor flags, flag register, or status register), internal buses, and sometimes special function units (the most common special function unit being a floating point unit for floating point arithmetic).
Some computers have more than one processor. This is called multi-processing.
The major kinds of digital processors are: CISC, RISC, DSP, and hybrid.
CISC stands for Complex Instruction Set Computer. Mainframe computers and minicomputers were CISC processors, with manufacturers competing to offer the most useful instruction sets. Many of the first two generations of microprocessors were also CISC.
RISC stands for Reduced Instruction Set Computer. RISC came about as a result of academic research that showed that a small well designed instruction set running compiled programs at high speed could perform more computing work than a CISC running the same programs (although very expensive hand optimized assembly language favored CISC).
DSP stands for Digital Signal Processing. DSP is used primarily in dedicated devices, such as MODEMs, digital cameras, graphics cards, and other specialty devices.
Hybrid processors combine elements of two or three of the major classes of processors.