I read as a young child he has the elephant head because parvarti made him out of clay and told him to watch so no one came near while she bathed. Her husband shiva came home and ganesha stopped him, he was so angry he cut off the boys head. Parvarti was so upset she commanded him to go into the forest, kill the first thing he saw and bring it back as the boys new head. Turned out it was an elephant.