While updating some pluging or wordpress itself, wordpress is set into maintenance mode so users cannot visit the site during the update. It happened to me several times that I started an update which did not finish correct. After trying to access wordpress (even Admin) this is not possible due to the maintenance mode.
The fix for this is rather easy but you need FTP access to your webserver: In the root of your wordpress site there will be a file called .maintenance. Just delete (or rename) this file and your site will be available again.
Good thing to do if you notice that the upgrade is stalling, is to note at which point this happened. This is because that particular plugin wil not function correct. You need to remove the plugin folder and reinstall the plugin. Best is to do this using FTP.