The story begins with a king who believes that he has constructed a perfect system of justice. He allows fate and the accused to decide ones' own guilt or innocence. If the accused is innocent then he will choose the door that has the lady and will be married in front of the crowd. If the accused is guilty he will choose the door that has a ferocious tiger behind it and be ripped apart as punishment for his crime.
The king also has a beautiful daughter with a similar temperament who falls in love and has an affair with a man who is far below her social station. He hears of the affair and immediately has the man arrested.
The princess, hearing about this development, pays several people to find out which door holds the tiger and which holds the lady.She is tormented with her decision because she finds that the lady chosen for him is one whom she hates and is very jealous. She believes that her lover will be happy with his bride and forget her, but she also cannot bear the thought of him being ripped apart to his death in front of her very eyes.
On the day of this young man's trial he looks to the princess because he knows her and knows that she would do anything tho find out the identities that lie behind each door. She raises her hand indicating that he choose the door on the right. The story ends here and the reader is left to decide which door was chosen. It is a great example of ambiguity.
Enotes provides a great summary at the link provided below. Basically the story is about a jealous princess who falls in love with a lowly man of whom her father does not approve. Her father imprisons him and the princess is left with a choice to allow her love to be killed or married off to someone else. The author allows the reader to decide how the story might end.