In a fight with Guru Parashuram, he threw an axe at Lord Gajanan which was a gift to him by his father. So to honor this gift, Ganesha chose to bear the axe’s blow instead of destroying it. Ganesha thus lost one his tusk, but gained humility and modesty.
“Aum Ekadantaya Viddhamahe, Vakratundaya Dhimahi,
Tanno Danti Prachodayat॥“
Ekadantaya – The one with the single tusked elephant tooth.
Viddhamahe – who is omnipresent.
Vakratundaya – Curved trunk.
Dhimahi – We meditate upon and pray for greater intellect.
Tanno Danti – We bow before the one with the single tusked elephant tooth.
Prachodayat – Illuminate our minds with wisdom.
Full meaning : “We pray to the one with the single-tusked elephant tooth who is omnipresent. We meditate upon and pray for greater intellect to the Lord with the curved, elephant-shaped trunk. We bow before the one with the single-tusked elephant tooth to illuminate our minds with wisdom.”
Ekadanta referring to one tusk in the elephant face means that God broke the duality and made us to have a complete one-pointed mind.