This is the partition of the CPU that takes care of how information is controlled around the CPU, what parts of the CPU are to function in the correct given way, this 'correct' method is defined by the controlling unit of the CPU as this is the part of the CPU making decisions on how the CPU functions, this could be essentially named the, 'core' brain of the computer.
Arithmetic Logic Unit:
This is a unit of the CPU that takes care of all arithmetical operations that are are undergone throughout the usage of the CPU. As well as arithmetical operator handling, this unit also handles logical operators in general in the code that is passed through it.
Calculations that the CPU makes stores the information about the calculation in this part of the CPU. Answers from calculations would be stored in here as well as information regarding what makes up the calculation.
The CPU deals with various different inputs and ouputs, the important part of this is how the CPU does this. The computer provides the CPU with information about the giving program that wants to run (the input for the CPU), the CPU takes on board this information, does its necessary calculations and then provides an output.