When it falls
Ganesh Chaturthi falls on the fourth day (Chaturthi) of the bright fortnight of the lunar month of Bhadrapada, usually in August or September, and the main celebration runs for ten days, ending on Ananta Chaturdashi.
Which deity is worshipped
The festival is entirely dedicated to Ganesha, the elephant-headed son of Shiva and Parvati, worshipped as the remover of obstacles and the deity invoked at the start of any new undertaking — which is part of why his own birthday is celebrated with such scale.
Why it's celebrated
The festival marks Ganesha's birth, though the story of how he came to have an elephant's head is itself part of what devotees recall during the celebration: Parvati created Ganesha from turmeric paste (or clay, in some versions) to guard her door while she bathed, and when Shiva returned and was refused entry by a son he didn't recognise, he beheaded him in anger. To console the grieving Parvati, Shiva ordered that the boy be revived with the head of the first creature found — an elephant — making Ganesha whole again and establishing him permanently among the principal deities. The festival's modern large-scale public form, with community-organised pandals and processions, is largely credited to Bal Gangadhar Tilak, who popularised it in the 1890s as a way to bring people together across caste lines under British rule.
How it's celebrated
Clay idols of Ganesha, ranging from small home-sized murtis to enormous pandal centrepieces, are installed and worshipped daily with puja, offerings of his favourite sweet, modak, and the singing of aartis such as Ganesh Aarti. The festival closes with Ganesh Visarjan — a procession, often with music and dancing, that carries the idol to a river, lake or the sea for immersion, symbolising Ganesha's return to his cosmic origin and the impermanence of all created form. Mumbai and Pune host some of the largest public celebrations in the country, with idols and processions drawing enormous crowds.