The Piggy Bank will appear in your game at certain dates once you are past power level 5 - the level you see on Daisy's icon in the main garden.
The Piggy Bank will show for 72 or 96 hours at a time and when the Piggy Bank event is running you will see the icon at the top and middle of the screen:
When you first tap on the icon, you'll see something like this. Please note though that offers may vary and the price point shown here may not be the same as in your game:
During the time the Piggy Bank is active, whenever you spend Gems in Merge Gardens, the same amount will be added to the Piggy Bank. You'll see two amounts on the bar at the bottom; the lower amount shows the minimum amount of Gems that you need to have in the Bank to be able to 'open' it and the higher amount is the maximum.
If you choose to open the Piggy Bank, you'll pay the price shown and receive the same amount of Gems that you've spent as shown in the bar at the bottom. Your Piggy Bank will then upgrade to another offer. Each Piggy Bank event has 3 levels with increasingly good offers!