Ganesha is depicted here with the body of a man and the head of an elephant, having only one tusk. He holds the other tusk (broken) in one of his hands. His unique feature, besides the elephant head, is the large belly practically falling over his lower garment. On his chest, across his left shoulder, is his sacred thread in the form of a snake. The vehicle of Ganesha is the mouse seen here paying obeisance to his lord.
According to the strict rules of Hindu iconography, Ganesha figures with only two hands are taboo. Hence, Ganesha figures are most commonly seen with four hands which signify their divinity.
The physical attributes of Ganesha are themselves rich in symbolism. He is shown with one hand holding his broken tusk and the second holding a sweet (modaka) symbolic of the sweetness of the realized inner self. In the two hands behind him he often holds an ankusha (elephant goad) and a pasha (noose). The noose is to convey that worldly attachments and desires are a noose. The goad is to prod man to the path of righteousness and truth. With this goad Ganesha can both strike and repel obstacles.
His pot belly signifies the bounty of nature and also that Ganesha swallows the sorrows of the Universe and protects the world.
The image of Ganesha is a composite one. Four animals viz., man, elephant, the serpent and the mouse have contributed for the makeup of his figure. All of them individually and collectively have deep symbolic significance. The image of Ganesha thus represents man's eternal striving towards integration with nature. He has to be interpreted taking into consideration the fact that though millenniums rolled by, man yet remains closer to animal today than he was ever before.
Ganesha's large head is symbolic of the wisdom of the elephant. His large ears, like the winnow, sift the bad from the good. Although they hear everything, they retain only that which is good; they are attentive to all requests made by the devotees, be they humble or powerful.
An intriguing aspect of Ganesha's iconography is his broken tusk, leading to the appellation Ekdanta, Ek meaning one and danta meaning teeth. It carries an interesting legend behind it:
When Parashurama one of Shiva's favorite disciples, came to visit him, he found Ganesha guarding Shiva's inner apartments. His father being asleep, Ganesha opposed Parshurama's entry. Parashurama nevertheless tried to urge his way, and the parties came to blows. Ganesha had at first the advantage, seizing Parashurama in his trunk, and giving him a twirl that left him sick and senseless; on recovering, Rama threw his axe at Ganesha, who recognizing it as his father's weapon (Shiva having given it to Parashurama) received it with all humility upon one of his tusks, which it immediately severed, and hence Ganesha has but one tusk.
A different legend narrates that Ganesha was asked to scribe down the epic of Mahabharata, dictated to him by its author, sage Vyasa. Taking into note the enormity and significance of the task, Ganesha realized the inadequacy of any ordinary 'pen' to undertake the task. He thus broke one of his own tusks and made a pen out of it. The lesson offered here is that no sacrifice is big enough in the pursuit of knowledge.
An ancient Sanskrit drama titled "Shishupalvadha", presents a different version. Here it is mentioned that Ganesha was deprived of his tusk by the arrogant Ravana (the villain of Ramayana), who removed it forcefully in order to make ivory earrings for the beauties of Lanka!
The little mouse whom Ganesha is supposed to ride upon is another enigmatic feature in his iconography. At a first glance it seems strange that the lord of wisdom has been granted a humble obsequious mouse quite incapable of lifting the bulging belly and massive head that he possesses. But it implies that wisdom is an attribute of ugly conglomeration of factors and further that the wise do not find anything in the world disproportionate or ugly.