The waltz is a smooth, progressive dance in 3/4 or 6/8 time, done primarily in closed position. It first became fashionable in Vienna in about the 1780s, then spread to many other countries within the next few years. The waltz, and especially its closed position, became the example for the creation of many other ballroom dances. Subsequently, new types of waltz have developed, including many folk dance and several ballroom dance types.
In contemporary ballroom dance, fast versions of the waltz are called Viennese waltz.
International Standard Waltz has only closed figures; that is, the couple never leaves closed position.
Contrast American Style Waltz,in which some figures involve breaking contact entirely. For example, the Syncopated Side-by-Side with Spin includes a free spin for both the man and lady. Open rolls are another good example of an open dance figure, in which the lady alternates between the man's left and right sides, with the man's left or right arm (alone) providing the lead.
See http://www.centralhome.com/ballroomcountry/International-American.htm for a more information regarding the differences between International and American Waltz.
A typical waltz figure (from the man's perspective) starts lowered into the knees and travelling forward with a strong heel lead. Count 2 rises and is taken on the ball of the foot, and count 3 starts on the ball of the foot and lowers to the heel as the couple begins to lower in preparation for the next measure. A smooth rise-and-fall action is a primary characteristic of this dance.
Websites to refer to: