Problem decomposition is the problem solving strategy of decomposing a problem into a set of subproblems solving each of the subproblems,  and then composing a solution to the original problem by exploiting the solutions to the subproblems.  

This is a powerful idea because it allows an idividual to break a problem up into pieces to better understand the situation,  and then they can take their solutions to those problems and combine them to get the final solution to their problem.