The Story behind Buddha Belly
Buddha means "Enlightened One" - so there have been MANY Buddhas throughout history .. Buddha is a description, not a name. The Dalai Lama is a Buddha, so is Jesus etc.
The Buddha who is always pictured with the large belly was "Buddai" - also referred to as the "Laughing Buddha"
According to legend, Budai was a monk and there is a story that he was a very good looking enlightened monk. People came for his teachings but most of the people came for his beauty. To stop people from coming for his good looks, Budai ate until he was big and fat, so that people would only come for his wisdom and enlightenment.
Budai is often admired for his happiness, plenitude, and wisdom of contentment and folklore has it, that if you rub his belly, it brings wealth, good luck, and prosperity.
There are other stories around this though and the above is only one of them ... but the belly is primarily symbolic - depicting centredness, plentiful chi energy in the centre of intuition/Dantien.