NAT VPS? How do they work?

I see a lot of mega cheap deals here at http://list.lowendserv.net/ but a lot come with NAT IP instead of a dedicated IP.

Now, I've never worked on NAT IP's before, are they hard work or would it simply mean a shared IP and instead of listening on Port 80, you change the port to the assigned port?

So for example in my nginx server block, if I change port 80 to the one assigned, my website will work?

Thank you very much.