How is the billing in the Aura console laid out ?

The Aura console provides a great level of detail for the user and allows you to measure the costs on an interactive basis 

• The billing presents a breakdown of the costs per AuraDB Instance (see #1) and the number of hours is listed (see #2) to clearly allow you to verify and understand the costs.
• In case of discounts or credits (See #3) that are applied against your usage (to correct previous billing or a service issue) you can see them instantly when a coupon is applied against your account. 
• The total due is updated with the latest usage figures and can be consulted live (see #4) and it can present a credit or debit total amount.  

Finally please note that as highlighted here, so long as an AuraDB Instance is running (used or not) it will incur costs.