What is unique about the maiden behind the door in "The Lady or the Tiger?"
The maiden behind the door is specifically selected for the accused.
The semi-barbaric king has a very unique system of justice. He had an arena built with two special doors. Behind one door is a tiger, and behind the other is a lady. If the accused chooses the door with the lady, he is innocent. If he chooses the door with the tiger, he is guilty. That is the trial.
The king wants to make sure that whichever door he chooses, the accused is immediately punished or rewarded. The tiger is the fiercest that can be found, and the accused will immediately be mauled to death if he chooses that door. The audience assembled will get to see some fine bloodshed.
However, if the accused is innocent, he will choose the door with the fair maiden behind it. The king will have not just any maiden there, but the perfect maiden for the accused, specifically selected for him.
[The] ranks of maiden youth and beauty throughout the land were carefully surveyed by competent judges in order that the young man might have a fitting bride in case fate did not determine for him a different destiny.
If the accused man chooses the maiden, the audience will be immediately treated to a huge party as he weds his new bride. It does not matter, by the way, if the accused man is already married or seeing someone. He is just happy to be alive, and goes along with it.
Of course, the problem the princess has with this system is obvious. If she points her lover to the door with the tiger, he will die! Yet if she points him to the door with the lady, he will go to someone else. The princess is not the forgiving sort. The princess knows not just which door is which, but exactly who is behind that door.
It was one of the fairest and loveliest of the damsels of the court who had been selected as the reward of the accused youth, should he be proved innocent of the crime of aspiring to one so far above him; and the princess hated her.
It is supposedly a test of your view of human nature which one you think the princess chose. If you think she chose the tiger, you believe humankind is naturally malicious. If you think she chose the lady, your view about mankind is that people are generally good.