It is not a real alternative yet, as it does not load asset bundles or work directly with coroutines. However, you can set and get headers, read status code etc.
It should also work in places where the .Net WebRequest.Create has been disabled. Please test away and let me know if fixes/features are required!
Update: Now supports gzip encoded responses.
Update: Now supports Etag caching, fixed dechunking bug.
You use it to communicate between your Unity world and resources on the Internet. WWW doesn’t offer everything necessary though so there are other methods, this one looks pretty good. Another option is .Net, but I don’t think that works on IOS or web player.
There should be a bunch more documentation on unityweb though, it’d make it way more popular if it was easy to understand, easy to implement, and if there was an easy way to know its advantages.