Paul Dukas (pronounced doo-KAHSS) was born in Paris, France in 1865. He was not a very well-known composer. Part of the reason for this is that he was a perfectionist, and commonly destroyed his work before it was published.
In 1797, a German named Johann Wolfgang von Goethe wrote a poem that is thought to have been inspired by a very old Greek story called "Philopseudes" (pronounced fie-LOP-soo-dees) by Lucian. Goethe's poem was called "Der Zauberlehrling" (pronounced dair ZOW-ber-LAIR-ling), which, in English, would be "The Sorcerer's Apprentice".
The story is simple. A master sorcerer leaves his workshop, giving menial chores to his apprentice. An apprentice is someone who wants to learn to become a master at something (in this case, sorcery), so they agree to work alongside a master to learn what the master knows.
The apprentice is less than thrilled with his chores, and is tired of hauling water one bucket at a time. He decides to use magic to enchant a broom to do the hauling for him. He is successful, but he quickly realizes he doesn't know how to make the broom stop.
The apprentice finally decides that he can't stop the broom, so he takes an axe and chops the broomstick in two. Unfortunately, each half of the broomstick becomes a new broomstick and each one takes a bucket and continues getting water.
Finally, the master sorcerer returns, sees what the apprentice has done, and casts a counter spell to undo the damage and clean up the mess. The morale of the story clearly seems to be "don't attempt to use knowledge or skills that you haven't fully understood yet".
Dukas wrote this symphonic piece in 1897 (100 years after Goethe's poem). In 1937, his estate was contacted by Walt Disney. Disney wanted to include the piece in his 1940 film Fantasia. Interesting side note, evidently Disney wanted to release an independent film of Mickey Mouse playing the Sorcerer's Apprentice. It was Leopold Stokowski (the conductor and orchestrator for Fantasia) that convinced Disney to include it as part of the larger film.
Once again, we have another great example of leitmotif. To tell the story, Dukas uses themes for the characters and actions. For example, when magic is used, the theme sounds something like this: