You'll probably want to involve us, is the shortest answer that I can give.
Situations that result in us asking folks that have made positive contributions to leave are incredibly rare, and the dynamics leading to them tend to be pretty unique. You just sort of arrive at a point where you plainly can't envision a future with them participating happily without continuing to create an intolerable amount of disruption.
Expulsion is exactly what it sounds like, informing the user that they're no longer welcome to contribute to the site. This isn't new, in fact, we put a deliberate reason for it in the 'delete' dialog back when we overhauled it:
This user is no longer welcome to participate on the site is probably the least used reason, but it's the one you'd use if someone simply has to go.
It's a good idea to talk to a community manager prior to taking this action.
We're not going to second-guess you; you're the one closest to the situation and you probably know way more about the dynamic than we could learn in a reasonable amount of time. What remains is us helping you figure out the most ideal way to part ways, which often means helping with the communication, or other accommodations we might be able to make in order to help the user accept your decision.
We'll also need to be around in order to help you manage communication on your meta site when questions come up, especially if the removal is felt on multiple sites. As you may or may not know, we'll need to manually process deletion of users with more than 500 rep anyway, so it's nice to know it's coming and we have some context.
To answer your questions directly:
What changes does this section mean for us moderators?
None really. There's always been cases where moderation teams have simply exhausted all means and patience with a particular user, and escalate it to us, at which point we inform the user that they're no longer welcome on a site.
It's not common, but it does happen.
In which cases are we supposed to expel user, and how does it fit into the old 7/30/365 days escalation for suspensions?
The majority of these would be after the first year-long suspension, but there could be cases where things escalate more quickly. For instance, if a user made threats after being suspended for 30 days, we'd delete them and take measures to prevent their return.
What does expulsion actually mean?
Gone; no longer able to participate on a given site. The implementation of this might look like a super-long network-wide suspension, or it might just be the removal of their account - it depends. But they're losing all privileges to participate without hope of regaining them in the future.
Are we supposed to simply delete users? And if yes, is that actually reasonable as it complicates handling circumventing their expulsion?
That reason from the delete dialog that I highlighted does some additional magic (and that's all I'm going to say publicly), but please coordinate it with us if possible. "If they cross the line again then you'll probably have no choice but to expel them" is a good example (if said by us) of when you'd use that option more autonomously.
On Stack Overflow, we might not get consulted as often, as there are quite a few more users on their 'last chance' than anywhere else.
Is account expulsion site-specific or network-wide?
It would depend. Usually (and ideally) site-specific, e.g. cooking just brings out the vinegar in some people as a humorous example. But there might be cases where people just completely come unhinged. It's better to coordinate with us (though we do leave the option available).
So, it's not new, it just hadn't really been alluded to previously, and it's something that you can point to if you need to inform a user that you really need them to demonstrate that a path to them continuing successfully exists. Don't make threats, but at the same time, we're not going to hide the fact that we do have a last resort.
Fortunately, as I said, it's pretty rare. I'll answer any more questions in comments, if anyone has them.