The Nutcracker is a classical ballet in two acts. Pyotr Ilyich Tchaikovsky wrote the music and the balllet was first performed in St. Petersburg, Russia in December, 1892. The ballet itself wasn't a big hit but Tchaikovsky took some of the music and put it into a 20 minute Suite (a group of pieces played together) which became one of his most popular pieces. In 1940 Walt Disney used some of the Nutcracker Suite in his animated movie, Fantasia. People liked the movie so much that the ballet became popular again and was even performed for television in 1952. Since then the ballet has been performed all over the world and has become a Christmas tradition.
The story takes place on Christmas Eve. It starts with a party at the Silberhaus family's house. Their children are Clara and Fritz. One of the party guests is a strange man named Drosselmeyer. He brings wonderful gifts including a nutcracker in the shape of a soldier for Clara. Late that night the nutcracker comes to life and turns into a prince. He takes Clara to his magical kingdom, The Land of the Sweets. The beautiful Sugar Plum Fairy rules this land. She welcomes Clara and the Prince and then orders her subjects to dance for them. Many dances are presented including dances about coffee, tea and chocolate. At the end of the ballet everyone dances a waltz. Clara wakes up the next morning under the Christmas tree with her Nutcracker still in her arms.
Here are some videos that tell the story.
Tchaikovsky wrote The Nutcracker for an orchestra of strings, woodwinds, brass, and percussion. To this orchestra he added a celeste for the "Dance of the Sugar Plum Fairy". The celeste was a new instrument that Tchaikovsky discovered in Paris in 1891. It looks like a small piano, but it sounds like bells. Tchaikovsky snuck the celeste into Russia and he was the first composer to use it there.
Due to its popularity, the Nutcracker has been used for many many different things and in many many different ways.
In 1960 Duke Ellington recorded a jazz version of the Nutcracker Suite. You can listen to it here . There is also a great book about Duke's Nutcracker Suite by Anna Harwell Celenza.
Here are a few other examples of the way the music from the Nutcracker has been performed or used.