When your Wordpress website simply shows the error "Briefly unavailable for scheduled maintenance. Check back in a minute." it means that an upgrade process was interrupted.
As part of the automatic upgrade WordPress places a file named .maintenance in the installation base folder (folder that contains the wp-admin folder). If that file exists, then vistors will see the message "Briefly unavailable for scheduled maintenance. Check back in a minute."
To stop that message from being displayed to vistors, simply delete the .maintenance file (note that this is a hidden file). The automatic upgrade should be executed again in case it failed.