Lord Ganesha is an embodiment of wisdom and bliss. He is the Lord of Brahmacharis. He is foremost amongst the celibates. He has as his vehicle a small mouse. He is the presiding Deity of the Muladhara Chakra, the psychic centre in the body in which the Kundalini Shakti resides.
The significance of riding on a mouse is the complete conquest over egoism. The holding of the ankusha represents His rulership of the world. It is the emblem of divine Royalty.
Ganesha is the first God. Riding on a mouse, one of nature’s smallest creatures and having the head of an elephant, the biggest of all animals, denotes that Ganesha is the creator of all creatures. Elephants are very wise animals; this indicates that Lord Ganesha is an embodiment of wisdom. It also denotes the process of evolution—the mouse gradually evolves into an elephant and finally becomes a man. This is why Ganesha has a human body, an elephant’s head and a mouse as His vehicle. This is the symbolic philosophy of His form.
Once Ganesha & His brother Lord Subramanya had a dispute. The matter was referred to Lord Shiva for final decision. Shiva decided that whoever would make a tour of the whole world and come back first to the starting point had the right to be the elder. Subramanya flew off at once on his vehicle, the peacock, to make a circuit of the world. But the wise Ganesha went, in loving worshipfulness, around His divine parents and asked for the prize of His victory.
Lord Shiva said, “Beloved and wise Ganesha! But how can I give you the prize; you did not go around the world?”
Ganesha replied, “No, but I have gone around my parents. My parents represent the entire manifested universe!”
Thus the dispute was settled in favour of Lord Ganesha, who was thereafter acknowledged as the elder of the two brothers. Mother Parvati also gave Him a fruit as a prize for this victory.