Considering that most file systems these days allow spaces in paths, I'd guess you can safely remove the »On Windows« there. The amount of shell and build scripts on Unix-likes that die horrible deaths when encountering spaces is not funny. And well, yes, in a way that probably means that spaces in paths are not »supported« there, but you could then say the same about Windows. As well as using non-ASCII in paths.
It means "everything past here should not be parsed as a - or -- flag". If you have a file named "-l", then ls -- -l will show you that file, instead of doing a long listing.
Not everything's a script though. I avoid using spaces, so I'm in the habit of (outside of a script) not quoting; if I bump into a space within a path then by that point it's just quicker to escape it.
I've been able to successfully use / in the Win32 API with the exception of CreateProcess. I think the reason is that when you start an executable you may pass command line arguments starting with /