In Animal Crossing: New Leaf, I received a piggy bank from the Post Office as a reward for saving up 1,000,000 bells. I was wondering what it did, so I put it on my sleek table and touched it. I heard a Clink!, which was the sound of money. I checked my inventory, and I found that 1 bell had been deducted from the 99,999 that I already had. I kept on inserting bells into the piggy bank. Where do my bells go? How can I get the bells I put inside the piggy bank back?
The Piggy Bank does absolutely nothing but cost money. You cannot get the money back. And according to the IGN wiki it is unknown if there is a reward for putting bells in it: http://www.ign.com/wikis/animal-crossing-new-leaf/Piggy_Bank
It is a Lucky Item though and can contribute to your Feng Shui score no matter where you place it in the room: http://animalcrossing.wikia.com/wiki/Feng_Shui
In previous games it was also worth 7,777 Happy Home Academy points. But I cannot find proof of that for New Leaf but this guide suggests it is true for City Folk: http://www.gamesradar.com/cheats/16074/
Several forums posts also reference the fact that your bells are gone forever. They go nowhere: