With WordPress BETA releases you can check new coming features of WordPress and test them locally on your computer or somewhere else. Example: For testing WordPress 3.6 you can download its beta .zip file here, upload them to a hosting or locally on your computer server, configure them just like you do with WordPress stable release installation and check it. Or you can replace WordPress core files on any running WP website and check BETA release, but remember its recommended not to run any BETA release on a production website. This tutorial explains you how you can easily upgrade WordPress to recent BETA releases by installing and activation a simple WordPress plugin.
Recently WordPress.Org made a beta release of WordPress 3.6. The software is still in development and its recommended not to run it on a production website, you can check its new features and look locally on your computer or somewhere else. For testing WordPress 3.6, try the WordPress Beta Tester plugin (you will want “bleeding edge nightlies”). or you can download its beta .zip file here.