So can someone describe a tri bike?

I didn't even realize until recently that people ride bikes tailored to triathlons. I never thought about it I guess...

What's so special about them? Frame geometry? Gearing? Brakes (or lack of same)?

I went in a tri store a few months ago looking for something piddly and glanced around at the bikes, but they just looked like ass-ugly carbon road bikes to me, maybe smaller.

Just curious. I swam competitively for 8 or 9 years and love to ride, but I've always hated running (and can't for the time being) so I've never seriously considered triathlons. Part of my ongoing mid-life crisis seems to be enhanced competitiveness, so I'm sort of considering them now. But I doubt I'd get a special bike. And maybe I'd just fast-walk the run part.