Problem Space refers to the entire range of components that exist in the process of finding a solution to a problem. This range starts with “defining the problem,” then proceeds to the intermediate stage of “identifying and testing possible solutions” and ends with the final stage of “choosing and implementing a solution”. Plus, it includes all of the smaller steps that exist between these identified stages.
A simple example of this might be realizing that you don’t have the right clothes for a social event, identifying what you need and where to go to buy the appropriate clothes and then buying those clothes and bringing them home. In between these stages you also have to take into consideration other associated concerns like "what can I afford? What stores carry what I want to buy?" and then "how do I find the time to shop for what I'm looking for?"