The warning links to a page that provides more details: "Your browsing data is automatically deleted if your Chromebook is running low on space. If additional space is needed, non-owner profiles that have not been accessed for more than 3 months may be erased (including downloaded files)."
In Chrome OS, the owner is the first user who logged in using a Google account. He's the only user who can restrict sign-in access or switch to the beta/dev channels. Regular users don't have these permissions, but they can save files. Google's warning informs users that these files are temporary and they could be automatically deleted if the accounts are rarely used. Google recommends users to upload the files to Google Docs or another "web-based storage application", but it would be a much better idea to add a new feature that automatically saves files to Google Docs.
Chromebooks include a 16GB SSD that's mostly used to store system files and cached user files. User data is encrypted and some of the data is automatically synchronized (preferences, bookmarks, extensions, apps, passwords). To reclaim disk space, Chrome OS can always delete discardable data like browser cache, so it's unlikely that important user files are removed first.
{ Thanks, Cougar. }