Earlier quoted context omitted.
The "server" in "language server" does not mean "server you access over the network" but "other process (on your machine) your editor talks to". (This is just the spec for a protocol.)
Can it be on across the internet? So, Apple can or cannot set up an internet service for Swift? If I think I have a better version can I point my editor towards that? If I program in a couple of languages, do I need to get ahold of servers to install?
In theory, yes the protocol can be used across the internet, but that would raise plenty of issues (security being a huge one). This is designed so that any program, like an IDE, can get code analysis and more without having to build special handling for each of them.
> So, Apple can or cannot set up an internet service for Swift?
Again, in theory they could. But why would they do that? Just run the server locally and get all the information there.
> If I think I have a better version can I point my editor towards that?
Yes. You simply stop the currently running language server and start the one you want to use instead.
> If I program in a couple of languages, do I need to get ahold of servers to install?
Yes. Each language would, in theory, provide its own server to do analysis. Of course, your favorite IDE would likely be more than happy to start the server for you if it's not running yet (as it's just a small process that runs in the background).
If you want to see how this works in practice just grab Visual Studio Code and start editing a Typescript file. This is already in use there.