As best as I can tell this is actually a file named "Bar.pm" in a subdirectory named "Foo".

Same thing. The directory is considered to be part of the filename, really, as the distinction is often meaningless in practice, and files' actual names cannot contain forward slashes anyway, so there's no ambiguity.

Can this sort of thing go on to multiple levels? Like, could we have a module named "Utterly::Completely::Foo::Barred::Up" that would be defined in the "Up.pm" file located in the "Utterly/Completely/Foo/Barred" subdirectory (of a member of @INC, I guess)?

Yes. To give a random example from my system, App::Prove::State::Result::Test lives in a file named Test.pm in a (sub)directory called App/Prove/State/Result.

And, is that the only place where such a module could be found, or could it also be in a file of a different name and/or in a different subdirectory?

Yes, that's the only place where such a module could be found, though @INC may of course contain several places where Perl will look.

When I read a phrase like "..module Foo::Bar would be in a file named Foo/Bar.pm" in the original (2006) discussion, and coming from a perspective of not already knowing Perl and trying to learn, it makes me think that maybe 'Foo/Bar.pm' is talking about some kind of internal-to-Perl thing, and not the Unix file system. I prefer to call 'Foo' part of the pathname.

In any case, thanks for explaining. It is difficult, when you can work with Perl only sporadically, to distinguish between actual language syntax and customary usage. Now I feel like I have a better chance of understanding module calls.

And, is that the only place where such a module could be found, or could it also be in a file of a different name and/or in a different subdirectory?

Well, this is just a technicality that only applies to require, not use, but just for completeness: You could take a module, for example Try::Tiny, copy its Tiny.pm to e.g. /tmp, and include it via BEGIN { require "/tmp/Tiny.pm"; Try::Tiny->import() } and it'll work fine - not that it's recommended :-)

If you only use use and modules from CPAN, then yes, the directory structure is pretty well defined (some rare, exotic modules may do things differently). The relevant documentation is use, require and @INC.