The Notifications page has useful details, including the version of Moodle you're using, which you may need if you want to report a bug to Moodle.org (http://tracker.moodle.org). This page may also include a warning that your site may not be secured if the cron (the time-based job scheduler that runs predefined tasks) has not been run. Most often, you don't need to worry about this, because the cron is run automatically.
This page also displays a Moodle Registration button with a statement above the button, Please register your site to remove this button. You or your system administrator would have registered with Moodle.org when you first downloaded Moodle; however, it's a good practice to update your registration (I update quarterly) to help Moodle.org keep accurate Moodle global statistics, which you can visit at http://moodle.org/stats. (By the way, keeping on top of registering the site doesn't remove the button.)