Ganesh Chaturthi Special- Chapter 4- The Origins of Lord Ganesha

Another story regarding the origins of Ganesha and his elephant head narrates that, once, there existed an Asura (demon) with all the characteristics of an elephant, called Gajasura, who was undergoing a penitence (or tapas). Shiva, satisfied by this austerity, decided to grant him, as a reward, whatever gift he desired. The demon wished that he could emanate fire continually from his own body so that no one could ever dare to approach him. The Lord granted him his request. Gajasura continued his penitence and Shiva, who appeared in front of him from time to time, asked him once again what he desired. The demon responded: "I desire that You inhabit my stomach."
Shiva granted even this request and he took up residence in the demon's stomach. In fact, Shiva is also known as Bhola Shankara because he is a deity easily propitiated; when he is satisfied with a devotee he grants him whatever he desires, and this, from time to time, generates particularly intricate situations. It was for this reason that Parvati, his wife, sought him everywhere without results. As a last recourse, she went to her brother Vishnu, asking him to find her husband. He, who knows everything, reassured her: "Don't worry, dear sister, your husband is Bhola Shankara and promptly grants to his devotees whatever they ask of him, without regard for the consequences; for this reason, I think he has gotten himself into some trouble. I will find out what has happened."
Then Vishnu, the omniscient director of the cosmic game, staged a small comedy. He transformed Nandi (the bull of Shiva) into a dancing bull and conducted him in front of Gajasura, assuming, at the same time, the appearance of a flutist. The enchanting performance of the bull sent the demon into ecstasies, and he asked the flutist to tell him what he desired. The musical Vishnu responded: "Can you give me that which I ask?" Gajasura replied: "Who do you take me for? I can immediately give you whatever you ask." The flutist then said: "If that's so, liberate Shiva from your stomach." Gajasura understood then that this must have been no other than Vishnu himself, the only one who could have known that secret and he threw himself at his feet. Having liberated Shiva, he asked him for one last gift: "I have been blessed by you with many gifts; my last request is that everyone remember me adoring my head when I am dead." Shiva then brought his own son there and substituted his head with that of Gajasura. From then on, in India, the tradition is that any action, in order to prosper, must begin with the adoration of Ganesha. This is the result of the gift of Shiva to Gajasura.