Most sites are able to apply updates in the background. Background Update Tester checks your site for compatibility and explains any problems.
There are many reasons why your site is not able to apply updates, like issues with file permissions or the inability to communicate securely with WordPress.org.
Install this plugin to see the specifics for your site.
For more technical details see (these two)[http://make.wordpress.org/core/2013/10/25/the-definitive-guide-to-disabling-auto-updates-in-wordpress-3-7/] (blog posts)[http://make.wordpress.org/core/2013/09/24/automatic-core-updates/].
We think at least 80 percent of installs do support background updates. For those remaining sites, updates are disabled for fairly complicated reasons, like use of version control, lack of OpenSSL support, and issues with file permissions. The recourse to resolve these issues is very difficult for the vast majority of users. Unfortunately it just isn't something we can or should ask of all users. A non-technical user, if they have the access to address these issues, is more likely to break their site than fix it.