I can hibernate my laptop so it doesn't drain the battery when I'm not using it. What if I could hibernate individual programs, like my web-browser?
I usually have scores of web-pages open in my browser, and just having it open, even if I'm not actually using it, uses the processor -- often quite a lot of it -- and drains the battery.
So I might leave the house in the afternoon to go out and do some PhD writing at a coffee shop. I won't be using the browser there, and I don't want it to drain the battery, so it'd be nice if I could hibernate it.
That'd be quicker and easier for me than manually closing it down and then manually reloading it all, and guarantee that when I bring it back up everything is in the exact same state.
Current operating systems may have quirks that wouldn't make this feasible, but of course that doesn't mean there's anything inherently impossible about the idea.