A Waltz is a graceful ballroom dance in simple triple time which originated in Europe in 18th Century, and became popular in the 19th Century. It first became popular in Vienna and later spread to Europe.
When the Waltz first came out, many aristrocrats were hesitant to dance it because of its flamboyant and spirited movements. (That was compared to the previous dances they had then. These days, the Waltz is incomparable to such dances as the Tango.)
Waltz comes from a german word walzen, meaning to roll, turn or glide. The Waltz is to be danced in as light and lively a manner as possible.
Johann Strauss Jr is called "The Waltz King" because he wrote many waltzes. Perhaps his most famous one is "The Blue Danube". Chopin also wrote many Waltzes but in a totally different style to the 'classical waltz'. Some of them are reelingly fast (Minute Waltz) while others are slower and melancholy in mood.
For an example of how to dance a Waltz, follow this link: Waltz Steps