Interesting read. Here an example of a PAN call from Doc 4444:
15.2.3 Weather deviation procedures
15.2.3.1.1 When the pilot initiates communications with ATC, a rapid response may be obtained by stating “WEATHER DEVIATION REQUIRED” to indicate that priority is desired on the frequency and for ATC response. When necessary, the pilot should initiate the communications using the urgency call “PAN PAN” (preferably spoken three times).
Another good example of an "urgent message" that needs to be passed, concerning safety of own craft.