Hellbreach Dungeons are a new dungeon type that will be making its debut in Diablo 4 Season 5, Season of the Infernal Hordes. It’s pretty similar to Cellars and will act as a sort of introduction to the Infernal Hordes mechanic that is making its way to the RPG in the new season.
These dungeons will feature a boss fight at the end and will reward you with Burning Aethers that you can use to open chests and get a reward when you complete the dungeon.
Hellbreach Dungeons explained in Diablo 4 Season of the Infernal Hordes

Hellbreach Dungeons are a sort of mini-version of the infernal Hordes run. It will introduce you to the new mechanics that have made their way to the game and will contain similar mechanics as the hordes, like Offerings and a final boss encounter.
You will find these dungeons scattered throughout Sanctuary and you will be able to take them on at any given time. When you complete them the Hellbreach Dungeons will also drop Burning Aethers that you can use to unlock chests and claim rewards.
Moreover, before reaching the final boss you will get a chance to choose between Banes and Bonnes which will increase the difficulty of the encounter. If you choose to make the fight more difficult you will obtain better rewards once you clear the dungeon.
Once you beat the boss a chest will spawn, and you will need to use all th Burning Aethers that you have collected so far to open it.
Why should you be increasing the difficulty in Hellbreach Dungeons in Diablo 4 Season 5
If you have done the proper prep work for Season of the Infernal Hordes then it’s recommended that you try the Hellbreach Dungeon bosses on a harder difficulty. The improved rewards that you get from them are going to come in handy for the Infernal Horde dungeons later on.
However, if your build is having a hard time beating the boss, you can always run to choose the encounter on the base difficulty. But by doing this you will lose out on a higher drop rate for some of the best Legendaries and Uniques that Diablo 4 Season 5 has to offer.