Ganesha is the formless Divinity - encapsulated in a magnificent form, for the benefit of the devotee. As per Hindu mythology, he is the son of Lord Shiva and Goddess Parvati.
Gan means group. The universe is a group of atoms and different energies. This universe would be in chaos if there was no supreme law governing these diverse groups of entities.
The Lord of all these groups of atoms and energies is Ganesha.
He is the supreme consciousness that pervades all and brings order in this universe.
The essence of Ganesha is brought out beautifully by Adi Shankara.
Though Ganesha is worshiped as the elephant-headed God, the form (swaroop) is just to bring out the formless  (parabrahma roopa).
Ganesha's big belly represents generosity and total acceptance. Ganesha's upraised hand depicts protection. It means, 'Fear not, I am with you', and his lowered hand, palm facing outwards means endless giving as well as an invitation to bow down. This is also symbolic of the fact that we will all dissolve into earth one day. Ganesha also has a single tusk which signifies one-pointedness. Even the implements Ganesha wields are symbolic. He carries in his hands the 'Ankusa' (signifying awakening) and the 'Paasa' (signifying control). With awakening, a lot of energy is released, which without proper control, can go haywire. Ganesha, the elephant-headed God travel on something as small as a mouse? Isn't that so incongruous? Again there is symbolism that runs deep. The mouse snips and nibbles away at ropes that bind. The mouse is like the mantra which can cut through sheaths and sheaths of ignorance, leading to the ultimate knowledge represented by Ganesha!
He is,  'Ajam Nirvikalpam Niraakaaramekam.' This means Ganesha is  Ajam  (unborn), he is  Nirvikalpa(attributeless), he is  Niraakaar (formless) and he symbolizes the consciousness which is omnipresent.
Ganesha is the same energy which is the reason for this universe. It is the energy from which everything manifests and into which everything will dissolve.