The Tribunal is a system in which players can regulate each other. When you enter the tribunal, via the League of Legends website, you are presented with a case. The case one of the thousands of daily reports submitted after games by the in game client. You get the chance to look over the case and decide if the reported summoner was really at fault for the situation. You can then choose to Pardon, Punish, or Pass the case based on your judgment. You can read more on the mechanics and rewards of the new system here.
That is, of course, if you can get to the website. At the moment when I try to access the Tribunal page, I'm met with Gragas.
Summoners!
We’re almost ready to release the Tribunal to the world. Today, we’ll be conducting a pre-release of the Tribunal, and we’d like to invite all level 30 summoners to come participate! If you are unfamiliar with the Tribunal system or want to know more about how it works, click here to check out our F.A.Q. Use your best judgment when deciding on Tribunal cases, as your performance in these cases will affect how many more cases you’ll be given.
To use the Tribunal, follow this link to get started. Thanks for helping us test this exciting new feature!
-Tamat, Lead Community Manager, via the official forums. 
