My interpretation of what's been suggested is basically an ip you can port forward, as if you had a public ip.
For example, let's say you want to run a minecraft server for your friends from your home. You use this hypothetical service to get an ip you can use, and tunnel the needed ports in to your network (and ultimately, your minecraft server).
This couldn't be provided with a single ip, since at best that would limit you to selling off individual ports. The product becomes worthwhile if each customer has their own ip.