WorldWideWeb is an HTTP server from The Iconfactory. Craig Hockenberry made the app because it is becoming harder and harder to start a simple Web server as Apple was removing open source components like the Apache HTTPd in recent years.
The name, WorldWideWeb, is a homage to the world's first HTTP server, which was running on Tim Berners-Lee's NeXT computer. You can see that computer on WorldWideWeb's help page.
The app works: select a folder, and WorldWideWeb starts listening on port 8080 to serve the website inside the folder. Then you can visit that website by navigating to localhost:8080 in a browser.
In the recently released 0.8.2 update for Planet, we added support for WorldWideWeb. Click on one of your Planets, and you will find a new menu item Develop -> Open in WorldWideWeb. You can use WorldWideWeb to serve the locally built static site.
If you are developing your own template for Planet, now it is much easier to see the changes. After making any changes, click Develop -> Rebuild then you can see the updated site on localhost:8080.
WorldWideWeb is available on the Mac App Store for free: