Up to date as of October 16th, 2015.
Once you have detailed language information on content, configuration, etc, which is now widely possible in Drupal 8 (see the tidbit on language assignment), you can use this data to pull out content for specific languages.
Everything is in blocks now
While not a multilingual change, it is hugely useful for multilingual use cases that everything is in blocks now. The page title, branding, breadcrumbs, menus, navigation tabs, and so on. This make it possible to customize page content much easier using the blocks controls, effectively giving site builders all the powers around page content.
Brand new in Drupal 8 are language visibility conditions for blocks provided by Language module. This combined with everything being a block allows you to swap out menus per language or localize the branding of the site.
This option is made available if you have more than one configured language on your website. While prior versions of Drupal provided visibility settings based on user roles, content types, paths, etc. this is now expanded to languages too. Here you can pick specific languages, even multiple of them (applying in an or relation).