The dancing Shiva is known as Nataraja.

The term ‘Nataraj’ means ‘King of Dancers’. This cosmic dance of Shiva is called Anandatandava, meaning the Dance of Bliss, and symbolizes the cosmic cycles of creation and destruction, as well as the daily rhythm of birth and death. The dance is a pictorial allegory of the five principle manifestations of eternal energy: 
•Shrishti - Creation.
•Sthiti - State, or preservation.
•Samhara - Destruction.
•Tirobhava - Illusion.
•Anugraha - Release, Emancipation.

In the form of Nataraja, Shiva depicts all of these elements. 

Shiva has four arms:
•He holds a Damaru or a drum in his upper right hand. It symbolizes sound originating creation or the beat of the drum is the passage of time.
•He holds fire in his upper left hand, which characterizes destruction. Mostly accepted as destruction of all that is bad. Both these hands are on the same level or, on the same line. This shows that creation and destruction are both equal.
•The lower right hand shows Shiva’s protection from both evil and ignorance to those who follow the righteousness of dharma. This gesture is known as the Abhaya Mudra.
•The lower left hand is pointing towards His feet. It signifies upliftment and liberation. It also points to the left foot with the sign of the elephant which leads the way through the jungle of ignorance. Here, the attention is drawn towards the fact that life is graceful.

His right foot is pressed downward, expressing Tirobhava, or illusions in life; whereas, the left foot is drawn upwards, depicting Anugraha, or release from the illusions of the world towards enlightenment. The right leg is at the middle of the figure, which shows the preservation of a state, or Sthiti. It also holds down a demon, which can be perceived as the demon in all of us that shall be suppressed. 

As in Hindu scriptures, “It is a continual dance of creation and destruction involving the whole cosmos; the basis of all existence and of all natural phenomena.