NATARAJA/NATARAJ is a Sanskrit word NAT means dance and RAJA means the king.natraja
The statue of NATARAJA or the dancing shiva is a symbol of creation , destruction and protection.
Every part or mudra of the statue is a symbol, we can notice that Lord Shiva is dancing over a dwarf. The dwarf is a demon APASMAR, symbolizing IGNORANCE .
Shiva has shown his right hand in Abhayadana Mudra, symbolizing that one should not be afraid of and he is there to protect all.
pointing his left hand towards his foot which is raised in air , the left side is the side of heart, symbolizing that one should not be afraid of changes, as the heart is beating constantly unstable things will also change constantly.
Right leg and right hand (abhaya dana mudra) are stable, symbolizing that mind should be stable .
Unstable things keep on changing in life but the mind should be stable.
with his right Stable leg he is standing on ignorance (Dwarf / demon).
holding a Damru which is a musical instrument, symbolizing creation and Fire in the other symbolizing Destruction.
the ring on the boundary is a fire circle, symbolizing the cosmic cycle,” the creation begets destruction and destruction begets creation and so on.
The standing posture of Nataraja is in the form of a wave, Wave is symbolizing energy which can create, multiply itself or can even destroy the other wave which is not in the same pattern or say rhythm of righteousness .

waveform of dancing shiva