Ganah in Sanskrit means 'multitude.' Isa means 'Lord.' Ganesha literally means the Lord of all beings. He is the first son of Lord Shiva - the supreme Reality. He also is called by other names like Ganapati, Gajanan, Vinayaka, and Vighneshvara. 

Ganesha is described as having human form with an elephant's head. The trunk which springs from the head represents the intellect, the faculty of discrimination. Ganesh's large belly is meant to convey that a man of Perfection can consume and digest whatever experiences he undergoes. 

At the feet of the Lord is spread an abundance of food. Food represents material wealth, power, and prosperity. Besides the food is a tiny mouse. The mouse does not touch the food but waits for the master's sanction as it were for consuming it. The mouse represents desire. 

Kubera, the god of wealth, offered a dinner to Ganesha, who ate all the food that was prepared for the entire gathering of guests and still was unsatisfied. At this time Lost Siva, his father, offered him a handful of roasted rice, and on eating this Ganesh was immediately satisfied. The story is directive to mankind that man can never be satisfied with joys of material wealth represented  by Kubera's feast. The absolute fulfillment or peace comes by consuming your own vasanas which are the unmanifest desires in you.