Also helps when you may be changing what you're doing. You know all that annoyance you currently do with NGinX and Apache and whatever else where you write a very cryptic config file telling it what runs on what ports and in what directories and how to serve it? I would love to do less of that. I would love to not have to change it every time I put up a new little Ruby-on-Rails toy web-app. I would love to be able to just shove a new Rails or PHP or Sinatra or Node.js project into my github repository, have a simple cron job on my server check it out into my "checkouts" directory, and then not have to configure the web server for it.
These things are doable with current servers, of course. They're just a pain and involve writing a fair bit of code to make it happen. If you could subtract the "update your NGinX/Apache/whatever config" step, you'd eliminate a fair bit of the current friction.
This is more important for hobbyists than big sites. A really flexible server will never be quite as fast as a fully dedicated server (cf Mongrel_cluster versus, say, Passenger). But for hobbyists, it could be a godsend.
Newer hobbyists won't even have to learn how to deploy a Comet/FlashSocket/Websocket server from behind a reverse-proxy. I envy that.