Start-up. Before starting it can be used to grab attention, set up a problem to be solved, as a reinforcing assessment on previous work done or as a diagnostic device on the range of abilities within the class before you start.
Amplifies attention. Attention is a necessary condition for learning and clicker questions demand a response making students stay on task. They pay more attention because they expect questions to be asked, and when asked, they get that lift they need after ten to fifteen minutes of exposition.
Anonymity. Many students value the anonymity of the responses. They can check out their own knowledge relative to others without embarrassment. It’s a form of self-formative feedback.
Diagnostic feedback. Teachers/lecturers can use them diagnostically to assess the overall state of knowledge of the class. This, as Dylan William states, needs the use of clever 'hinge’ or diagnostic questions, that really do test understanding, as opposed to recall. This is precisely what Mazur does at Harvard with stunning results in attainment.
Sparks discussion. Results can be used for further remedial elucidation or to spark small group peer instruction. Again, this is how they are used in Mazur’s peer-instruction sessions.
Summative assessment. Quick reinforcing, summative assessments can be held at the end of the session.
Evaluation of session. It would take a brave teacher/lecturer to do this, but why not ask students to evaluate the session at the end. Could lead to improvements next time.