I found out about Tixati, through about.com. And I saw they were talking about how this is moving away from the whole "Tracker" idea. I don't really understand how this all works. I have a good grasp on networking, but I don't understand what they mean by no more trackers

What's exactly that article in about.com? Because trackless actually isn't only Tixati feature. Nowaday almost every torrent clients have got that feature.

Basically, torrent still works via DHT, PEX, and magnet links (in the case no tracker available).

About them:
lifehackercom/5411311/bittorrents-future-dht-pex-and-magnet-links-explained

But if you want to know more specific about how DHT works, and how your torrent client be able to find out the 1st peer without knowing about its info from something outside (like a tracker), then search and read about DHT bootstrap nodes. --> Similar topic: http://forum.tixati.com/support/417/