The explanation that I think wasn't entirely clear in the post is how it actually works/why that's better.

From what I can tell, the situation is this:

1. You have a host behind NAT

2. That NAT will not allow you to open ports via e.g. uPnP (because it's a corporate firewall or something, for example) so other tailscale nodes cannot connect to it

3. You have another host which has the same configuration, so neither host can open ports for the other to connect in

The solution is to run a peer relay, which seems to be another (or an existing) tailscale node which both of these hosts can connect to via UDP, so in this circumstance it could be a third node you're already running or a new one you configure on a separate network.

When the two NAT'ed hosts can't connect to each other, they can both opt to connect instead to this peer node allowing them to communicate with each other via the peer node.

Previously this was done via Tailscale's hosted DERP nodes; these nodes would facilitate tailscale nodes to find each other but could also proxy traffic in this hard-NAT circumstance. Now you can use your own node to do so, which means you can position it somewhere that is more efficient for these two nodes to connect to and where you have control over the network, the bandwidth, the traffic, etc.