S'rî Ganesha is that aspect of God who is the remover of obstacles. He is a manifestation of S'iva and worshipped in the beginning of any auspicious performance for blessings (see Ganesha Invocation). A unique combination of his elephant-like head and a quick moving, tiny mouse vehicle represents tremendous wisdom, intelligence, and presence of mind.
In the Vedic literature there is a story that tells about the origin of Ganesha in which he was created solely by his mother Parvati. The story begins with the fact that Ganesha's father, Lord S'iva was out on penance, so when Parvati wanted a child she created him herself by taking all the dirt from her body and forming it into the shape of a boy. So thus Ganesha was created.
The story continues, to say that one day Parvati wanted to take a bath and she told her son to keep guard outside the door and to let no one, without exception, into the room. At the very same time that Ganesha was keeping watch for this mother and respecting her wishes, Lord S'iva came back from his penance and demanded to be allowed in so that he might see his wife. Ganesha following strict orders from his mother and not knowing that S'iva was his father, told him steadfastly 'No'. S'iva, enraged, cut off the little boy’s head.
Upon seeing her little boy headless, Parvati became furious and told her husband that she would destroy the universe if he was not brought back to life. S'iva ordered a servant to go out and search for the first head he found and to bring it back for the little boy. The servant set out, and not being too brilliant brought back the first head he found, which happened to be an elephant's head. This is how Ganesha has a little boy's body and an elephant head.