Vinayaka means that he is totally master of himself. He has no master above him. He does not depend on anyone. He is also called Ganapathi. This term means he is the lord of the ganas - a class of divine entities. This term also means that he is the master of the intellect and discriminating power in man. He possesses great intelligence and knowledge. Such knowledge issues from a pure and sacred mind. This knowledge leads to wisdom (vijnaana). Because he is the master of Buddhi (intelligence) and Siddhi (wisdom or realization), he is described as the Lord of Buddhi and Siddhi. Buddhi and Siddhi are referred to as the consorts of Vinayka.
The mouse is the vehicle of Vinayaka. What is the inner significance of the mouse? The mouse is considered as the embodiment of the sense of smell. The mouse is a symbol of the attachment to worldly tendencies (vaasanas). It is well known that if you want to catch a mouse, you place a strong-smelling edible inside the mouse-trap. The mouse also symbolizes the darkness of night. The mouse can see well in the dark. As Vinayaka's vehicle the mouse signifies an object that leads man from darkness to light. The Vinayaka-principle, thus, means that which removes all the bad qualities, bad practices and bad thoughts in men and inculcates good qualities, good conduct and good thoughts.