Office Online already offers real-time collaboration on file editing between multiple people, and that feature has been promised for the desktop version of Office 2016, but it hasn't showed up in the previews so far. The latest update to Office 2016 brings it a lot closer.
As the official Office blog explains, while full collaboration in the desktop apps hasn't happened yet, some of the indicators are positive:
While Real Time Typing will ship in subsequent builds, we are rolling out a key part of that collaborative experience with Real Time Presence. Real Time Presence allows you to see where in a document your teammates are editing.
Initially, that option will be rolled out to OneDrive for Business users, which makes sense -- collaboration is going to require some form of centralised storage even if the apps manipulating the files are running locally.
Office 2016 on Windows Preview update [Office Blog]