Ganesh is the elephant-headed God who removes obstacles and brings good luck

Ganesh is the son of the Mother Goddess Parvati. While protecting his mummy, young Ganesh had to go into battle where his head was chopped off. To quickly save his life, the Mother Goddess had to replace his head with an elephant's head. Hindus always worship Ganesh first because he removes all obstacles and brings good luck. They worship him before they start anything new, like joining a school, or going on a journey, or celebrating a festival. Ganesh is not only brave, he is also very wise. Hindu children learn about the importance of being brave and wise from the stories of Ganesh.

Reference: Primary Hinduism by Seeta Lakhani (Ch.2, 'Thinking About God', p.26)