This competency is key to the practice of business analysis. It is about finding the true root cause of any problem so that the solution options you consider indeed address the real cause of the problem at hand.
Another key aspect of problem-solving is ensuring that all stakeholders have a common understanding of the underlying issues. It ensures that all points of view are addressed and identifies any conflicts that might exist between the stakeholder group's individual goals and objectives.
An easy way to remember what problem-solving is to remember that in the context of business analysis, it can almost be described as just another phrase for business analysis. Think of all the requirements you develop, analyze, and find solutions for as a form of problem-solving.
Another part of problem-solving is ensuring all assumptions are identified and validated. The final part of problem-solving is ensuring alternative solutions to a problem are considered and potentially developed further.