The Vinayaka principle has only one meaning, which is relevant to everyone regardless of whether he is a believer or non-believer. Vinayaka means that he is his own master, he has no master above him. He is also called "Ganapathi". The term "Ganapathi" means he is the Lord of the Ganas - a class of Divine entities. The term also means that he is the master of the intellect and the power of discrimination in man. Such knowledge issues forth from a pure and sacred mind. The knowledge leads to Vijnana/wisdom. Since he is master of Buddhi (intelligence) and Siddhi (realization), he is described as the Lord of Buddhi and Siddhi. Buddhi and Siddhi being personified as the consorts of Vinayaka.
(Divine Discourse, 12 Sept '91)