What purpose does a use case diagram primarily serve?

A use case diagram primarily serves the purpose of illustrating the interactions between users (also known as actors) and the system. It provides a visual representation of how users will engage with the system to achieve specific goals. This diagram helps stakeholders understand the functional requirements by depicting various use cases, which are the specific scenarios in which users will interact with the system.

By focusing on these interactions, use case diagrams facilitate clearer communication among project teams, helping developers and stakeholders identify necessary features, user needs, and potential improvements. This clarity is crucial during the requirements gathering phase, ensuring that all user interactions are accounted for and that the system will effectively meet its intended purposes.

In contrast, the other options relate to different aspects of systems and software design. Showing software structure relates more to class diagrams or component diagrams, depicting how software components are organized. Depicting object states over time is focused on state diagrams, which show how the state of an object changes in response to events. Detailing the flow of control in a system pertains to activity diagrams or sequence diagrams, which illustrate the dynamic behavior of a system rather than user interactions. Each of these elements is vital in its own right, but they do not convey the primary emphasis of a use case diagram.