The play 'Aladdin' tells the story of a poor boy, Aladdin, who comes into possession of a magic lamp containing a genie after a magician tricks him. After enduring various challenges, including being trapped in a cave and then taken to a desert by the magician, Aladdin uses his wit to reclaim the lamp and return home with the help of the genie. Ultimately, Aladdin marries a princess, gains wealth, and outsmarts the magician, ensuring a happy ending for him and his family.