The newest element in Season 5 are Set Dungeons. As you complete the goals of Season 5, you are rewarded with pieces from one of the class sets. For Barbarians, it's the Might of the Earth set. Each set has an associated Set Dungeon which requires you to complete tasks utilizing that set.
For example, the Might of the Earth set requires you to kill a Frozen enemy every 10 seconds for 1 minute. Now the only way a Barbarian can normally freeze an enemy is by using one of the Earthquake variants, which has a 60s cooldown. But the 4-piece bonus of the set has your Leap trigger an Earthquake when you land. So to fulfill that requirement, you have you take the Earthquake variant, and then Leap fast enough to kill enemies quickly.
There is another requirement as well which similarly takes advantage of the set's properties. The set dungeon is timed.
One thing that wasn't clear is that you only need to meet one of the requirements to complete the dungeon, not both. I unnecessarily quit several times when I failed a requirement early. But in the end I decided to explore the whole dungeon, and it turned out that I was successful enough to finish the Set Dungeon and qualify for the season's rewards.
It was an interesting piece of content. To be honest, it's aimed at the crowd that runs a little higher than I do. I think I've only collected one other full set, on my Crusader.
All in all, though, it was a pretty enjoyable season.