Apache is *A* webserver but it is not *THE* webserver. Think of this feature as making TNet a very, very, very stripped down version of Apache. This feature makes TNet its own webserver (though very limited, don't expect to host websites with it :p)
I'm no web programmer and have very little experience in this area, but you could do something like this:
test.php:
http://pastebin.com/RDDGHPdk (had to upload to pastebin as html tags aren't allowed on this forum, even when enclosed in bbc code tags)
This would create a button that - when clicked - will send the "Shutdown=1" message to the TNet instance running on 127.0.0.1:5127.
You would then have to write some code on TNet's side to handle this message. I don't have TNet 3 so I can't provide an example for that, but maybe someone else can.
You can either install php (w/ curl) on your own computer and run test.php from your web browser, or you can upload test.php to a web host (that has php and curl support already) and use it from any computer.
This featue is useful because it enables you to build a web interface to remotely administrate your TNet server. It could serve many other uses as well if you get creative with it, such as having a website w/ a live leaderboard or a live feed of what's happening in your game.
Also, System.Net isn't available on mobile devices, right? So this feature could make TNet usable on mobile devices assuming it doesn't use the System.Net namespace. Also, you'd have to flesh it out a bit to add support for POST requests as GET isn't suitable for sending a lot of data, but still, it'd be a big step forward.