Go to: Admin panel -> Settings -> Tickets -> and check the box next to "Web Tickets Priority"
This will allow users to overwrite or set their own priority no their tickets opened via the web interface. You may also want to consider using "Emailed Tickets Priority" which will set the tickets priority based on the priority of the email that is sent when utilizing email to open tickets (thus letting the user set their ticket priority when then author and send their email to the system).
I personally do not use these settings, because I find that users over inflate the priority of their issues and cannot adhere to the agency level priorities that we have defined internally.