We're all familiar with the problem of port-forwarding and NAT: if you want to expose something to accepting an incoming connection, you need to configure port-forwarding on the router or conjure up some other black magickery to "punch holes" in the firewall using UDP or something. I'm fairly new to the whole "hole-punching" concept so could someone explain how it works?

Essentially, I'd like to understand how hole-punching would work and the theory behind it, as well as if two TCP connections could be bridged via a third party. Since there's no issue with outgoing TCP connections since it's handled with NAT, could a third party bridge the connections so that the two parties are still connected but without the bandwidth cost of traffic going through the third party?