Like numerous other aspects in Hinduism, deep symbolism is attached to the elephant head of Ganesha. The big elephant head of Ganesh represents the great repository of wisdom. The large ears symbolically suggest that it is the medium to acquire vast knowledge.
The trunk symbolizes the power to uproot ignorance. It also symbolically suggests the discriminatory capacity to differentiate between the dualities of life.
The two tusks represent the dualities of life and the broken tusk represents shedding of duality.