Making your way to the Shattered Sanctum will allow you to eventually find the Defiled Temple and if you proceed further, a room with a puzzle can be found.
Once you have gotten passed Priestess Gut and a large ogre named Polma, you can check out the puzzle and attempt to solve it.
Solving the puzzle in the Defiled Temple will open up an entrance to the Underdark, allowing you to continue exploring or continue with your quests.
Defiled Temple Puzzle Hint
While some may have thought that the puzzle was merely based on logic, it appears that a hint can be found within the Shattered Sanctum.
If you remember where you find Dror Ragzlin during his attempt to speak to a dead Mind Flayer using a spell, there is a room nearby that has a hint for the puzzle.
From the two doors that lead to where Dror Ragzlin is, if you make your way west from both entrances, you will find a hint for the puzzle on a wall. (Goblins are present)
Defiled Temple Puzzle Solution
To solve the puzzle, you can sort to the hint as a clue of how things should look but this is rather inverted depending on the angle you are looking at it from.
Instead of trying to copy the puzzle, keep in mind that there is a light shining from above, and solving this puzzle can easily be remembered by shining a light onto the dark.
This means that you can simply solve the puzzle by making sure that all the empty sockets or black circles are on the same circle where the light shines.
Alternate Solution To Open Underdark Entrance
Just near where the entrance is supposed to open, you may find that there are items that you can interact with, and this includes a lever near the puzzle.
If you make your way north of the puzzle, your characters may go through a Perception Check, which will reveal the lever.
You can have one of your characters pick the lock on the lever, which will allow you to open the passage and skip solving the puzzle.
Verdict
Using the lever to open the path to the Underdark will not yield any rewards but can be a quick way to get into the Underdark if you need to.
If you skip the puzzle solving, you can come back later to complete it to get Inspiration as well as bonus experience for completing this.
The Defiled Temple is one of the areas that contains an entrance to the Underdark and there are also more that can be found.