We've already learned about the officials and the referee in the last tutorial. They are responsible for interpreting the rulebook and calling penalties on players and teams when the rules of the game are broken.
A challenge requires a review of the previous play through something called instant replay. Instant replay is technology in lots of sports around the world that allows for the officials and fans to see the previous play from various angles and perspectives. This helps the referee to ultimately make his final decision. You'd be amazed at how much slow-motion and a different perspective adds to an ice hockey game.
Here are the rules of challenges in ice hockey: