It is the address at which you receive the bill of your credit card and the one with which you have registered with the credit card company - your current address.
It is an important verification tool for online payments and is checked in order to make sure that the right person is making the purchase.
Other tools such as the expiry date of the card as well as the CVV at the back of the card are used for verification purposes.
The web stores from which you purchase are very interested in this address since this is the address that will confirm you as the rightful owner of the card.
Image Courtesy: newremotecontrol.com
This is the address to which the goods that have been purchased are to be delivered. This can be your home address or some other address as per your preference. If you are looking to present someone with a gift, you can get the item gift wrapped and sent directly to their address.
It is important to mention the shipping address since without it, the order cannot be processed and you may face a delay.
Image Courtesy: bluetreepublishing.com