Automatic Updates

Auto-updates are only done between minor versions, as Andrew said. So 3.7 will go to 3.7.1 automatically, but it will not go to 3.8 automatically, since that’s a major version.

So for example:

YES: 3.7 -> 3.7.1 -> 3.7.2, 3.7.3 etc.

NO: 3.7 -> 3.8 -> 3.9 etc.

If you want to enable auto-updates for major versions (like 3.7 -> 3.8) you can do that, but it’s a little risky for a production machine where you probably want to test plugins first:

http://www.wpbeginner.com/wp-tutorials/how-to-enable-automatic-updates-in-wordpress-for-major-releases/