Decomposition is where you break down the complex problem into the system. Each smaller part can then be examined or solved individually since they are simpler to work with.
An example of decomposition:
Solving a crime on its own can be a very difficult task.
The crime is a complex problem and this needs to be broken down into smaller problems that the police officer would need to know the answer to solve the problem. These could include:
What was the crime
Is there any witnesses
Where and what time the crime was committed
What evidence is there
These problems can be solved much easier and can be examined in much more detail. Once the police officer has all the information from each simpler problem they might be able to solve the crime.