Lord Ganesha’s huge body represents the Cosmos or Universe and his trunk the Pranava or OM, the symbol of the Brahman. His elephant's head denotes superior intelligence and the snake around his waist represent cosmic energy. The noose is to remind us that worldly attachments are a noose. The rosary beads are for the pursuit of prayer and the broken tusk is symbolic of knowledge as it is with this tusk that he is believed to have acted as the scribe who wrote down the Mahabharata as dictated by the great Sage Ved Vyasa. The sweet in his hand is to remind us of the sweetness of one's inner self. The physical form of Ganesha is corpulent and awkward to teach us that beauty of the outward form has no connection with inner beauty or spiritual perfection. Ganesha, on his vehicle, the mouse, symbolizes the equal importance of the biggest and the smallest of creatures to the Great God.
Another version is that Parvati had prayed to Vishnu for a son and that when one was granted to her she was so proud of him that she called together all the gods to admire him. All the gods duly gazed at the beautiful child except Sani (Saturn), who looked down at the ground, for he was under the influence of his wife's curse, which caused any being that he fixed his eyes upon to be burnt to ashes. Parvati, however, thought that her son was immune to such dangers and insisted that Sani look at him and admire. So Sani looked, and Ganesha’s head was burned to ashes. Parvati now turned on Sani and cursed him for having killed her son, so that he became lame. But Brahma comforted Parvati and told her that if the first available head were put on her son's trunk he would be able to restore his life. So 'Vishnu set forth on Garuda and the first creature he saw was an elephant sleeping beside a river. He cut off its head and brought it back to Parvati. Yet another version that makes Parvati creator of Ganesha says that during one of the twilight periods between the ages a number of unworthy people had obtained access to heaven by visiting the shrine of Somnath, with the result that heaven was full to bursting while the hells were empty. lndra and other gods asked Shiva for his help in rectifying this situation. On his advice they approached Parvati, who by rubbing her body produced a being with four arms and an elephant's head who would induce in people a desire for riches so strong they would never think of spending their time in pilgrimage.