Within the Circuit, you can visit the paddocks to check up on the health, statistical values, and more of each Chocobo participating in the day's events. In addition, you can check the boards to see the odds as they are figured for each race. Then, you speak with an NPC and place your bets, choosing the two birds you predict will place 1st and 2nd (in any order, so long as you have the right ones).
To be honest, I didn't think twice when I read that this was being added to the game. However, being as bored as I was last night, I decided I would go visit and see what there was available. I was, in a word, addicted. I spent a good few hours running from the grandstands to the betting areas. I bet on numerous races, and I got a kick out of dragging a few friends to the Circuit with me. We sat around chatting in between races, we heckled the passersby, and we shouted at the Chocobos during their sprints toward the finish line.
I've never been a gambler, but I loved doing this. I lost repeatedly at first, not knowing how to properly pick the birds. As I figured out the charts and saw some of the trends, I started making better picks. I did actually win one race, picking the correct two birds. Not a massive amount of gil, but I did win enough to put me back ahead of when I showed up.
Overall I think the Chocobo Circuit will be a nice way to kill time when not doing anything terribly progressive. In practical terms, time spent staring at my Moogle while chatting with friends can be converted into time spent watching the races. Certainly more interesting than the inside of our Mog Houses, yes?
Pics from my first day at the races: