He has four hands, an elephant's head,winnowing pan like ears, a big belly and a beautiful body of red complexion. His vehicle is a tiny mouse. In his hands he carries a rope (to carry devotees to the truth), an axe (to cut devotees' attachments) and a sweet dessert ball-ladoo/ modak (to reward devotees for spiritual activity). His fourth hand's palm is always extended to bless people. This indicates that those who surrender themselves to Ganesha's mercy need not fear anything.
Ganesha's bulky head symbolizes his extraordinary intelligence. His ears are broad like winnowing pans. You know winnowing-pans are used to winnow grain. What happens then? The husk and the grain get separated. So Ganesha distinguishes between truth and untruth. It may also be said that the broad ears symbolize his capacity to listen to the prayers of all his devotees with great attention. His ever-moving trunk teaches that one should be active always, his single tusk denotes single-mindedness in action. His huge belly signifies that the entire Brahmanda (Universe) is hidden within Ganapati.
He rides a rat. The rat personifies evil qualities like anger, too much of pride and selfishness. Riding on the rat shows that Ganesha checks these evil passions. A unique combination of his elephant-like head and a quick moving tiny mouse vehicle represents tremendous wisdom, intelligence and presence of mind