Arithmetic-Logic Unit: the portion of a computer's central processing unit that performs integer arithmetic and logical operations, such as bitwise AND, OR, NOT, and XOR. The instruction decode logic of the CPU determines which particular operation the ALU should perform, the source of the operands, and the destination of the result.
The width in bits of the words which the ALU handles is usually the same as that quoted for the processor as a whole whereas its external busses may be narrower. Floating-point operations are usually done by a separate floating-point unit. Some processors use the ALU for address calculations, such as incrementing the program counter, others have separate logic for this.