As I mentioned earlier, product managers work to add value to users and the business. The problem space is where your user needs are. This could be the challenges/pain-points they face, their goals or their desires.
'Customers don’t care about your solution. They care about their problems’ - Dave McClure
It is a product manager's role to ensure the product allows users to overcome their problem or achieve a goal. However, people don’t often communicate what their problem is in a clear way. We often think of solutions because as users we don’t know any better (e.g. asking for a feature because they think it will help, rather than being clear why they want that feature. Product Managers must read between lines to define the problem space.
Getting the balance between adding value to users and adding value to the business is known as product / market fit.
An image of the product market triangle. From Dan Olsen’s book. Resources section.
Target Customer: Who are they?
Underserved Needs: What are their needs?
Value Proposition: How the customer benefits and how our product is better.
Feature Set: The functionality that supports those benefits.
User Experience (UX): What the customer interacts with to get the benefits