Ganesha Chaturthi also known as Vinayaka Chaturthi, is the Hindu festival celebrated on the birthday (re-birth) of Lord Ganesha, the son of Shiva and Parvati.
It is believed that Lord Ganesh bestows his presence on earth for all his devotees during this festival. It is the day Shiva declared his son Ganesha as superior to all the gods, barring Vishnu, Lakshmi, Shiva and Parvati. Ganesha is widely worshipped as the God of wisdom, prosperity and good fortune and traditionally invoked at the beginning of any new venture or at the start of travel. The festival, also known as Ganeshotsav ("festival of Ganesha") is observed in the Hindu calendar month of Bhaadrapada, starting on the shukla chaturthi (fourth day of the waxing moon period). The date usually falls between 19 August and 20 September. The festival lasts for 10 days, ending on Anant Chaturdashi (fourteenth day of the waxing moon period).
While celebrated all over India, it is most elaborate in Maharashtra, Andhra Pradesh, Karnataka, Goa, Orissa, Tamil Nadu and Chhattisgarh. Outside India, it is celebrated widely in Nepal and by Hindus in the United States, Canada, Mauritius, Singapore, Thailand, Cambodia, Burma , Fiji and Trinidad & Tobago.
Legend
Traditional stories tell that Lord Ganesha was created by goddess Parvati, consort of Lord Shiva. Parvati created Ganesha out of sandalwood paste that she used for her bath and breathed life into the figure. She then set him to stand guard at her door while she bathed. Lord Shiva returned and, as Ganesha didn't know him, he didn't allow him to enter. Lord Shiva became enraged and asked his follower ghosts to teach the child some manners. Ganesha, being born of Parvati, the embodiment of shakti or power was very powerful himself. He defeated the ghost-followers (called as the "gana"s)and declared nobody was allowed to enter while his mother was bathing. Sensing a growing turmoil, the sage of heavens, Narada, along with the Saptarshi (the seven wise rishis) went to appease the boy with no results. Angered, the king of Gods, Indra attacked the boy with his entire heavenly army but even they didn't stand a chance. By then, this issue had become a matter of pride for Parvathi and Shiva. After the devas were defeated, the trinity, the controller, preserver and destroyer of the universe launched an attack against Ganesha. Amidst the fight, Shiva severed the head of the child. And brought on Parvathi's rage. Seeing her son dead, Parvathi revealed her true self, as the Adi-shakti, the prime energy that fuels the universe and sustains matter. Taking on a terrible form, she vowed to destroy the universe where her son was killed and re-create a better one. The Gods prostrated before her and Shiva promised that her son will live again. The trinity hunted the world for a head and came across a mother elephant crying for her dead baby. They consoled the mother and fixed the head of the baby elephant in place of Ganesha's head. Lord Shiva also declared that from this day, the boy would be called as "Ganesha" (Gana-Isha=lord of the Ganas). In this way, Lord Ganesha came to be depicted as the elephant-headed God.
Lokmanya Bal Gangadhar Tilak
Founder of Sarvajanik Ganeshotsav
The public celebration of the Ganapati festival -- Sarvajanik Ganeshotsav -- was started by Lokmanya Bal Gangadhar Tilak in 1893.
The well known freedom fighter and statesman, Lokmanya Bal Gangadhar Tilak, realized that Ganesh Festival would be a way of uniting people in a common cause and in this manner a possible means of bringing about political consciousness under the guise of a religious celebration, with freedom for India being the ultimate goal. He started celebrating Ganeshotsav as a public festival by establishing a Sarvajanik Ganpati at Vinchurkarwada in 1894 and today it is the most popular event in the State.
Reference: http://en.wikipedia.org/wiki/Ganesh_Chaturthi