Automatic background updates were introduced in WordPress 3.7. An email notification is sent (subject line below) following the success or failure of the update.
Subject: [Your Site Name] Your site has updated to WordPress ?.?.*
There is no need to configure anything from your end.
Background updates are a valuable feature of WordPress, ensuring sites receive bug/security fixes quickly. By default, only minor releases – such as for maintenance and security purposes – and translation file updates are enabled on most sites. However in special cases WordPress may update your plugins and themes.
So for example WordPress will automatically update 3.7 to 3.7.1 or 4.4.1 to 4.4.2. WordPress will not automatically update from 3.7 to 3.8 or 4.4.2 to 4.5 as this would be a major update.
We at LJC also check your sites for major WordPress updates, plugin updates and theme updates as part of a maintenance package to ensure all the components continue to work well together.