What do I do with the piggy bank?

You don't do anything. It's a way to make you spend money by releasing the gold bars.

Your piggy bank can only hold so many gold bars. When you have accumulated something like 32 gold bars, your piggy bank is full. If you tap on the piggybank, it goes to a page, where you can buy the gold bars in the bank. I haven't checked closely enough yet, to see if buying gold bars this way, is actually a good deal or not. You can just ignore these graphics, if you are not interested in buying the gold bars. However, it is just one more thing, in the game, taking up precious time, if the clock matters....like, when you are using a starcat & you only have the starcats assistance for only 30 minutes.