Gajantaka is a fierce form Shiva. In this form he dances on the head of an elephant and kills it. Elephant in Hinduism is symbolically represents prosperity and material possession. Through this dance Shiva exhorts the devotees to stay away from fickle wealth, prosperity and happiness. He is asking his devotees to aim for eternal bliss.
It is said that in this dance, Shiva kills the elephant and wears its skin on his body. Thus he is the one who wear Gaja Charma or elephant skin.
The elephant was chosen as a symbol because it is associated with Goddess Lakshmi and Indra. Man is constantly chasing wealth. He is never satisfied with wealth.
As Gajantaka, Shiva completely breaks free of all material things.