Ganesha, Ganapati, Vinayaka, Vigneshwara are the countless names of the visible manifestation of the essence of the words ‘That Thou Art’ – Tat Vam Asi.
…the elephant-headed remover of all difficulties in life indeed represents the highest and the best that have ever been given in our scriptures.
….on the spiritual pilgrimage, all the obstacles are created by the very subjective and objective worlds in the seeker himself; his attachment to the world of objects, emotions and thoughts, are alone his obstacles. Sri Vigneswara chops them off with the axe and holds the attention of the seeker constantly towards the higher goal with the rope that He has in this left hand. En route, He feeds the seeker with the modaka – the joy of satisfaction experienced by the evolving seeker or reality) – and bless him continuously with greater and greater progress…. (Swami Chinmayananda)
Lord Ganesha represents
The significance of riding on a mouse is the complete conquest over egoism. The holding of the ankusha represents His rule of the world. It is the emblem of divine Royalty. (Swami Sivananda)