Billing address is the one which is used to generate invoice for any particular order while shipping address is the address which is your to deliver your order.

When you add your shipping address, you can select a check box for ‘Set as Billing Adress’ to set this address as your billing address. In case you want to set another address as billing address, you can click on edit button available for any address you wish and select the check box to set it as your new billing address. If you have not selected any address as your billing address, by default your shipping address for that order will be used as billing address.