A problem is any question or matter involving doubt, uncertainty, or difficulty. To explore the problem space begins with accepting that one’s vision is at least partly obscured by the fog of perplexity. The idea is to keep moving, following the light, while mists clear and the landscape reveals itself. Exploring the Problem Space/About
Problems are problems because they conflict with desired outcomes. Exploring a problem space may start with the desired outcome (universal but affordable health care!) or with a "problem-alert": the sense that something is wrong. Part of exploring a problem space is refining, clarifying, or figuring out what the desired outcome is. Part of that process is refining, clarifying, or figuring out what the actual problem is. Some problem-alerts may turn out to be false alarms.
I've been told that focusing on problems is negative. Some people have encouraged me to adopt mindfulness instead, i.e., to practice non-judgmental awareness of the present moment as a way of being. To which I respond: that is magical thinking. Besides, exploring a problem space can be fun. Live the problem.