The significance of the Nataraja sculpture is said to be that Siva is shown as the source of all movement within the cosmos, represented by the arch of flames. The purpose of the dance is to release men from illusion, and the place where it is said to have been performed, Chidambaram, called the centre of the universe, is in reality within the heart. The gestures of the dance represent Siva's five activities (pañcakrtya): creation (symbolized by the drum), protection (by the 'fear-not' pose of the hand), destruction (by the fire), embodiment (by the foot planted on the ground), and release (by the foot held aloft).
Fonte: Encyclopædia Britannica.

God is the cosmic dancer. Siva is the primal soul, Paramejvara, as power, energy, and life of all that exists. This is Siva's intricate state of Being in Manifestation. Nataraja is the dance of the entire cosmos. It is the rhythmic movements in all. All that is, sentient and insentient, pulsates in his body. Nataraja is art and spirituality in perfect oneness, chosen to depict the divine because in dance, that which is created is inseparable from its creator. Similarly, the universe and the soul cannot be separated from God.
Fonte: University of Rochester.

Nataraja (literally, The King of Dance) is the dancing posture of Lord ?iva, the aspect of God as the Destroyer in Hinduism.
Fonte: Wikipedia.

Riassumendo: per la religione hindu Siva ha creato l'universo danzando. Nataraja è Siva il dio della danza. Diceva Nietzsche:

crederò solo in un dio che danza