As far as I know, the identity is just a public key. You can add contacts only by either scanning a qr-code disayed on your contact's phone in person or by being introduced to each other by a mutual contact, so there is no real need for discovery. As there are no servers at all (not even federated), this also means that no one can even enumerate users.
"No servers" doesn't feel quite right -- no dedicated servers, maybe, but the project depends on TOR, which has quite a lot of servers. I've not dug into the source, but I'm expecting each client to be using a TOR hidden service to allow peer-to-peer connections.
The ability of TOR to allow essentially roaming services like this is a feature I'm always surprised isn't used more often. And although it's not something I was ever going to actually get around to, something like Briar has been on my list of interesting thins to try to do for a while -- I'm really glad someone else has had a similar thought and been able to run with it :).
