This is an obvious reference to the elephant's tusks. The tusks are actually the elephant's incisor teeth.
Elephants use their tusks to dig for food, as well as weapons when fighting.
Both male and female African elephants have tusks, but only male Asian elephants have tusks that actually protude out beyond the lips. Not all male Asian elephants have tusks, however. 40-50 percent of male Asian elephants are born tuskless. These elephants are called makhnas in India. They are about 5cm long at this stage.