Your question refers to understanding whole concept and principles of VirtoCommerce solution development and it is very difficult for me to answer your question simply even though we have the article that will explain the general solution development process based on the VirtoCommerce platform, but I am afraid that this article is far from the ideal state.

In addition of this article I’ll try to get you more intuition about overall extension model principles in more briefly form.  

Here is architecture overview diagram where you can see what storefront is just one of possible clients that can use the platform through API calls. 

Our storefront is standalone application ever written by using different technology stack (ASP.NET Core) while Platform application still use (.NET 4.6).

Both applications - platform and storefront have separate development and release processes and different extension models:

Platform – is extended only via new modules and doesn’t allow any direct existing code changes. 

Storefront – is extended by direct solution code modifications.

To start storefront customization you need to make fork of latest storefront code (do not download a zip as you did)  into your own GitHub repository and perform changes there.  For publish you changes to Azure app you may use any preferred ways described in these articles on official Microsoft documentation.

I hope my answer was helpful and clarified the situation a bit.

(Eugeny Tatarincev)