Bharata Natyam is one of the Classical Indian dance forms (others include Kathakali and Mohiniatam from Kerala, Odissi from Orissa, Manipuri from Manipur, Kathak from Uttar Pradesh, Kuchipudi from Andra Pradesh) originating in the southern state Tamil Nadu. Although Bharata Natyam originated in Tamil Nadu, it is conceived both locally and globally as the dance form of all of all of India. Even its name suggests this: "Bharata" means India in Sanskrit, while "Natyam" means dance. Perhaps its popularity is due in part because it became a powerful tool for nationalists to convey goals of freedom from the British during the Freedom Movement in India. But that's a topic for a whole other essay entirely.
The three main elements of Bharata Natyam, as set forth by the Natyasastra (an ancient and detailed text describing drama) include: natya, dancing using dramatic acting and gestures; nrtta, decorative or abstract dance; and nritya, dominated by mudras (hand gestures) that convey a specific narrative.
The ability of the dancer to tell stories through specific gestures and facial expressions is a central aspect of Bharata Natyam. Mudras aid in the telling of stories; they are used to portray certain gods, goddesses and animals, as well as actions and states of mind. The dancer is not merely a dancer, but also a dramatic actor, utilizing expressions to arouse rasa, a sentiment or mood, from the spectators. Abhinaya, or expression, is used to provoke rasa, and thus is an important tool for past and contemporary choreographers/dancers alike. It involves the use of eye movements to clue the spectators into the meaning of danced gestures by directing their gaze to a specific place or part of the body.
The Natyasastra, while laying down very detailed rules about dance, leaves a lot of room for artistic expression; each chapter concludes with a statement saying that the artist has the freedom to go beyond its prescriptions. Even with the popular "traditional" dances taken from the Puranas, Ramayana, or Mahabharata, choreographers still have their own interpretations. The same story is never performed the same way twice because each guru has their own version.
Bharata Natyam is typically performed with a live orchestra, including a vocalist, mridangum (drum), flute or violin and natuvanga (cymbals). The orchestra typically sits on the left side of the stage. The dancer wears temple jewelry, make-up and a modified sari-like costume. The arangetram is the debut/graduate performance of a dancer once they have mastered the form. Recitals usually include a Pushpanjali, Alaripu, Jatiswaram, Shabdam, Varnam, Padam and Tillana.