An ALU is an Arithmetic Logic Unit.  It is a fundamental building block of any CPU processor in today's computing world.  Logically, its performance and application are relatively simple to understand.  Two integers in bit form are applied to the input of the ALU, and another terminal receives the instructions for manipulating said input. These instructions, as the units name implies, are mathematical calculations such as addition or subtraction.  Once the ALU has performed the commanded manipulation, it outputs the correct value.

The two inputs are more appropriately called operands, or the information to be operated on.  The instruction for the required operation is known as the opcode.  Modern ALU devices can perform a lot of simple functions on the operands provided.  In addition to basic adding and subtracting, they can shift data left or right, invert data, AND OR data, send data through untouched, increment or decrement by 1, rotate the data in some fashion, and still many more possibilities.  The only requirement that most designs have on the ALU is that these operations remain very simple and fast.  For more complex mathematical requirements often there is a higher level processing circuit, which utilizes the simple mechanisms of the ALU to come ultimately up with the answer, but the ALU itself does not perform these complexities.