In broad terms, the Problem Domain describes the area undergoing analysis. The scope of the problem domain needs to be identified upfront by the business analyst.  The size and scope of the problem domain can vary greatly depending on the goals of the project being undertaken.  The scope may align with the boundaries of an entire organization or it may be much more granular, aligning with a single organizational unit, a specific business process, or a particular system.

Even when the scope of the problem domain aligns with the boundaries of a particular group or system it may also include stakeholders outside of the process or organizational group such as customers, suppliers, or any other stakeholder which provides an input or accepts an output of a process, organization, or system.

In short, the Problem Domain is anything and everything that is needed to define the area under analysis, fully understand the inputs and outputs of its processes, and achieve the goals of the area under analysis, but nothing more.