Ganapathy is the leader of the Ganas, ie. the leader of groups, tribes, race, army, escorts, and hence Lord Siva’s first son is described as the supreme leader (Vinayaka). He is also known as Vigneswara – Lord of all obstacles. These names clearly show that He is a master of all Circumstances.
Ganapathy is represented as yellow skinned, short with a big round belly, elephant headed with one trunk, four arms, large ears and bright shining eyes.
In popular Hindu mythology, Ganesha is considered to be the son of the Hindu deity Shiva and Parvati. The most common account of his birth begins with Shiva leaving his wife Parvati for an extended period of time in order to meditate upon Mount Kailasa. This inspired intense loneliness within the goddess. Longing for a son, she gave birth to the young man, Ganesha. She quickly ordered him to stand guard at the door of her private chamber while she bathed. Eventually, Shiva returned from his meditation and attempted to access Parvati's private chamber. Ganesha refused to let him in and a struggle ensued, after which Shiva beheaded Ganesha. Hearing the commotion, Parvati came out of her bath and informed Shiva that he had just killed her child, and threatened to destroy the universe if the situation was not rectified. Shiva promptly sent his servants to the North, the holy direction, so that they could find a new head for Ganesha. Details as to where this replacement head came from vary according to different sources. Eventually, the servants found an elephant and cut off its head, which they placed upon Ganesh's shoulders upon their return. When Ganesh came back to consciousness, Shiva adopted him as his own.
Puranic myths provide a wide variety of other explanations for Ganesha's form. Some texts say that he was actually born with his elephant head (or heads), though in most stories he acquires the head later. In a different story, when Ganesha was born his mother Parvati showed off her new baby to the other gods. Unfortunately, the god Shani (a deity corresponding to the planet Saturn) – who is said to have the "evil eye" – looked at him, causing the baby's head to be burned to ashes. The god Vishnu came to the rescue and replaced the missing head with that of an elephant. In yet another story, Ganesha is created directly by Shiva's laughter. After Ganesha's birth, Shiva became concerned that the youth was excessively beautiful, and so he cursed Ganesha to have the head of an elephant and a protruding belly in order to make his appearance less appealing.
The Skandapurana says that Ganapathy was formed from the dirt collected from the body of Goddess Parvathy. Devi created an extraordinary elephant headed creature with four arms and deputed him to safeguard the entrance towards the Chandraprathishta, which was being performed in heaven.
As per the Matsyapurana, Lord Siva had the habit of peeping while Goddess Parvathy had her oil bath. On one occasion Devi come across the peeping Siva. Though her husband, she did not like this action of his. Parvathy thus created a figure out of the dirt she had washed away from her body and give breathe to it by sprinkling water from theGanges. As usual Siva tried to enter the bathing place of Parvathy. The guard didn’t allow him in. Furious, Siva cut the guard’s throat. Fearing Parvathy’s anger, Siva swiftly went out. He saw an elephant there, cut down its head and fixed it to the body of Parvathy’s creation. Thus was born Parvathy’s son, the elephant headed Ganapathy.
According to the Padmapurana, Parvathy, like all of God’s creations, had the desire to give birth to a son who would be the embodiment of all virtue. For this she prayed to God Vishnu who appeared before her. He granted her wish by taking birth in her womb. The son thus born to Parvathy is Ganapathy.
The Uthararamayana, portrays Siva and Parvathy as a couple who were interested in novel ways of sexual intercourse. One day they accepted the posture of an elephant, and thus was born the elephant headed Ganapathy.