I'd guess it's a sign of prosperity and happiness in some cultures. Mind you there are a lot of statues of the buddha where he's pretty trim.
Maybe the fat buddha is a particular icon of a specific buddhist culture.
The area of the abdomen just below the navel is called the Tan Tien or Hara in Eastern philosophy and is said to be the centre of the body's Chi, or Life Force. Perhaps the Buddha has an abdundance of Chi and so the abdomen is bigger.
There are many Buddha images showing the Buddha in all sorts of condition, including some depicting hime so thin all his rib bones are showing through. I guess many people feel comforatble with a nice fat jolly image than a starving one.
A folk figure of an itinerant Chinese monk named Ho-tei is widely referred to by non-Buddhists as the "laughing Buddha" or "happy Buddha." According to some beliefs he is an incarnation of a Buddha who will appear in the future and might properly be called a bodhisattva.