Core automatic upgrade feature was introduced in WordPress Version 2.7. While doing automatic upgrade WordPress places a file named .maintenance in your website’s root directory.
The file is shown during automatic and manual updates made from WordPress admin section. But sometimes when WordPress fail in completing the update process (especially when your PHP memory is hitting its resources or during some communication error etc), it keeps showing, “Briefly unavailable for scheduled maintenance. Check back in a minute.” message on every page of your website.
To stop this message from being displayed to your website visitors, you just need to delete .maintenance file. The automatic upgrade should be executed again, just in case it failed.
If that file exists in your base folder, then visitors will see the message, “Briefly unavailable for scheduled maintenance. Check back in a minute.” and will not be able to access your website.