We need to understand the iconography of deities always at three levels: 1 Mythology 2. Metaphysical symbolism 3. Aesthetics. There is perhaps no end to possible interpretations of such a glorious image!
I quote two beautiful sources. The first is from Ananda Coomaraswamy, the authority on Shiva and iconography. From his book, The Dance of Shiva, 1918:
The second I scanned from my copy of E.B.:
Legend ( provided by Rshankar of Rasikas.org):
The iconography of Siva as natarAja is rather complex and here's some of what I've understood.
Siva is depicted as holding a battle axe (mazhu), a deer (mAn), a ball of fire, and a damaru in his hands, with a cobra for a garland, and tiger-skin as his lower garment.
All of these were invoked from the sacrificial fire by the 3000 (tritIya sahasra) ascetics (dIkshta) of the taDavana of cidambaram and thrown at the sky-clad (digambara - in other words, naked) youth that had the rishi-patnis following him. They did not realize that it was Siva who had come to teach them the error of their ways. He grabs the cobra and uses it as a garland, the deer with sharp horns is tamed and held in his hand, as are the battle-axe, the ball of fire, and the damaru - as Siva rattled the damaru, all the languages of the world emerged (vAcikam sarva vAngmayam), and he kills the tiger, skins it, and covers his lower body. The final assault from the ascetics comes in the form of an evil dwarf called muyalakan - Siva subdues him and dances on his back - and as he does that, the amazed ascetics realize their folly and lose their ego and ignorance and become enlightened- so the dwarf symbolizes ignorance and by dancing on him, Siva destroys ignorance.
Another aspect to the iconography is the reference to the five elements (panca bhUta):
He holds the fire
The gangA symbolizes water
His long locks capture the wind/air
His feet are on the dwarf who rests on the earth
The moon symbolizes the sky/ether.
