WP Cron doesn’t work until someone visits your site. If your job is scheduled to run at 1pm but there are no visitors until 6pm, then your job will start at 6pm. Improved Cron solves this by faking a visit to your site every minute.
The ‘Stop’ button will cause the background process to die next time it wakes up (within 1 minute). The ‘Refresh’ button just reloads the page, checks the status and updates the time values. As with the Cron View, or Cron Gui, plugin you can see the currently active cron schedules as well as the registered intervals (mostly useful for developers).