The ALU, or Arithmetic Logic Unit, is a section of the CPU (Central Processing Unit) dedicated to working with Arithmetic and Logic...
It can process a variety of mini-tasks (operations) and is used in conjunction with other parts of the CPU, such as the Control Unit, within cycles of the CPU (clock-cycles). During the execute part of the Fetch-Decode-Execute cycle, it takes in data / operations (usually stored in registers) and spits a result out (back into a register). In essense, it is the brain of the CPU.