Hi Jessica(i hope that is the name!!!),
Basically you dont need a website if you just want an mobile commerce store. But, essentially, you need a website along with your mobile commerce app for the following reasons:
1) To manage product/inventories
2) To provide marketing and after sales support
3) Various marketing tools like push-notifications etc. are best and easy to send via a web application.
There can be many more, but these are coming straight off my mind right now.