(Actually I should be drafting a FOSDEM talk about this right now, but I'm having a £1.50 draught beer & on FB instead. Gotta <3 České dráhy.)
Kids — i.e. in the Douglas Adams sense anyone under about 35 -- are more used to phones and tablets. The next billion people to come online will know nothDouglas Adams sense anyone under about 35ing else.
I reckon OSes will become more like Android, iOS, and ChromeOS — self-updating, without a "desktop" or much in the way of local storage or rich window management (for instance, see what's happening to GNOME) and fairly useless unless connected to the Internet and various invisible servers off in the "cloud" somewhere.
Some "apps" will run locally, some will be web apps, some will be display sessions on remote servers. There will be little visible distinction.
We'll have no local admin rights, just the ability to put on sandboxed apps that only interact via the online connection. No local storage, or just a cache. No software updates; the OS will handle that. No easy way to see what apps are running or where.
What'll drive this will be sky-rocketing costs of supporting rich local traditional OSes.
It will have the side-effect of blurring the lines between a workstation, a laptop, a tablet and a phone.
For some current examples, see the Red Hat Atomic Workstation project, Endless OS, and SUSE Kubic MicroOS. Read-only root FS, updates via a whole-system image pushed out periodically. Only containerised apps are allowed: there's not even a local package manager.