Challenge Rifts are randomly generated dungeons accessible via the Challenge Rift Entrance in Westmarch. To complete a Challenge Rift you need to kill a certain amount of enemies and then defeat the Rift Guardian, all within the time limit of 15 minutes. None of the enemies in Challenge Rifts drop any loot, instead you get Rift Progress Globes and Energy Globes when you kill elite monsters. Rift Progress Globes reduce the amount of monsters you have to kill before the Rift Guardian is summoned, while Energy Globes reset your cooldowns immediately.
Completing a Challenge Rift in time will give you a one-time reward of runes and Honor. It will also unlock the next level of Challenge Rift with stronger enemies and greater rewards. You can choose to replay a lower level Challenge Rift, but you only get rewards when you beat a level for the first time.
You can see the Challenge Rift leaderboards for each class, showing players who completed highest level Challenge Rifts in the shortest time.
There's also a general all-class leaderboards where you can see how different classes compare to one another.
Challenge Rifts are supposed be the final testing grounds for your character!