that is an elephant. the story goes that he originally was one of the sons of shiva. he had a contest with his brother kartik, about who could race around the universe the fastest and come back. kartik went ahead, travelled the entire cosmos and came back, but ganesha was smart. he simply did a revolution around his parents: lord shiva and goddess parvati - because to him, his own parents were his 'universe', because he loved them so much.  kartik became furious because he lost, and he cut off his brother's head with his dad's (shiva's) axe. lord shiva became furious, punished kartik to make revolutions around him and his mother for the rest of eternity, and replaced his son ganesha's head with an elephant head (because he couldn't find a human head in time).    h_chaturthi
Canada