During the installation or when the site is on the update mode, such error (503 Server Error) can appear. In order to solve this, please, remove the file maintenance.flag in the root of the system.

Magento shows Error 503: Service Temporarily Unavailable page after extension installation via Magento Connect or scheduling a backup:
Service Temporarily UnavailableThe server is temporarily unable to service your request due to maintenance downtime or capacity problems. Please try again later.

Cause If you see this page (along with default Magento logo and styling), the store was switched into Maintenance mode, by maintenance.flag file in root directory. Most likely "Put store on the maintenance mode while installing/upgrading" checkbox was enabled during extension installation in Magento Connect Manager:

When this option is checked, maintenance.flag file is created in the root directory of your store and store switched on the Maintenance mode.

Another possibility to trigger Maintenance mode was to enable Put store on the maintenance mode while backup creation option when scheduling new backup:

To turn the maintenance mode off you need to delete the maintenance.flag file via FTP or Filemanager: