Kathak is one of six distinct styles of Indian classical dance. It has roots in story telling..the word “katha” comes from Sanskrit for story. Although it originated in the temples of ancient India, Kathak was adopted in the courts of Mughal kings. As many as 150 ankle bells ( ghungru ) are worn to emphasize the flamboyant and intricate footwork. Kathak resembles Spanish flamenco dancing apparently because it was exported via the Romani people, thought to have originated and migrated from the Indian subcontinent around the 11th century!
Kathak incorporates three styles: natya , expressive or dramatic dance; nritta , pure and abstract dance which is often highly rhythmical; and nritya , the fusion of these two elements.
The link I chose is an exuberant, more modern interpretation. If you like it, check out a more classical clip from the same dancers, Nirupama and Rajendra: Dance India 2010