In plain words
His elephant head and his mouse mount demonstrate the truth that divinity is present not only in human beings but in the animal world as well. Moreover, the elephant head is a symbol of intelligence. The elephant is very intelligent. That is why the expression ‘elephant's cleverness’ came into use. Whatever the situation, an elephant does not forget its master. Until it breathes its last it shows gratitude towards its master; it will protect its master even at the risk of its life. In the elephant the quality of forbearance too is abundant.
Forbearance is Satya; forbearance is Dharma; forbearance is the Veda, forbearance is Ahiṃsā, forbearance is yajña; forbearance is joy, forbearance is heaven; forbearance is all in all the worlds.
Once an elephant enters a dense jungle with no path to walk on, a path is made for people. In the same way, if you keep the elephant-faced Lord before you, you can easily cross the forest of life.
Kuḍumulu and uṇḍrāḷḷu: the inner meaning
On this Vināyaka Caturthī we offer kuḍumulu and uṇḍrāḷḷu to Vināyaka. Vināyaka does not partake of food cooked with oil. He accepts only food cooked over steam, without oil. What is the inner meaning of cooking rice flour, putting jaggery and sesame flour into it, making kuḍumulu and uṇḍrāḷḷu and offering them to Vināyaka? Those who eat food cooked by steam without oil stay in full health. Health itself is great good fortune. But man today, through the craving of the tongue, gets hooked on many kinds of tastes and ruins his health with his own hands. Food cooked over steam is digested quickly. Eating rice flour cooked over steam, mixed with sesame, prevents diseases of the eye.