Similar to Facebook Connect, it would allow administrators to build sites on other domains and by including a file/provide a login and password, you can plug into an XF installation and pull information as needed via API calls.
For example, I can have DomainA be my XenForo installation and DomainB would another site that does not have an XF installation on it. If I want to build a customized experience, I could simply include a file from DomainA and include it on DomainB.
Once that's done, the user could simply log into the site on DomainB and all their information (username, avatar, email, usergroup permissions) get passed to it. If I want to get any other information, I can use a simple call to get posts or threads by them, but mainly I can then know who a user is on DomainB and handle it how I want.