computer:/// is a special location that the GVFS daemon responds to. For more information on what GVFS is, see What is gvfs and why should I want it on my system?, but suffice it to say that it's a wrapper over the raw POSIX calls for reading, listing, and writing files, and it provides some nice abstractions. Visiting
computer:/// will work in any GVFS-enabled application.
You may manipulate GVFS locations, including
computer:/// (at least IIRC) on the commandline with the
gvfs-* family of tools.
Now, that's in GNOME 3. You're on MATE. I'm not entirely familiar with MATE's software stack nowadays -
computer:/// used to be a special thing that Nautilus responded to, not the underlying file read daemon (or the underlying calls, if you like). I'm not sure how far MATE's come from ditching busted GNOME 2 technologies (yes, I know MATE is about making GNOME 2 live on, but there's a lot of old stuff that still needs to be replaced under the hood, like libbonobo, libunique and some other libraries that no one actually understands anymore). So, depending on that, the answer is either: "it's a hack in Nautilus" (old) or "it's a bit of a hack in GVFS that Nautilus inherits" (new).