This is my azure payasyougo usage cost for this month.
I'm struggling to understand why I would be charged for a Standard Medium App Service, I would of thought that it would be included in the compute hours? I have only one Cloud Service running and this seems a bit steep for a cloud service that is not doing much...
Any suggestions?
While pricing is off-topic, I think I can answer this from a general operational angle (even though this will likely be closed since it's not programming-related).
As your graphic shows, you are consuming resources for different services. Compute-hours equates to your virtual machines that you've deployed, and you're consuming those resources whether you're using 0% or 100% CPU / memory / network, whether you've deployed code or not. They are allocated and, as far as Azure is concerned, deployed for your use, no matter what you're doing (or not doing) with them.
When you created your App Service, that was yet-another set of resources deployed. And another set of resource-hours you're consuming (again, whether you use 0% or 100% is irrelevant).
Same thing would happen if you created a database instance or any other Azure service: You'd pay in whatever way is described for that particular service. And each service has its own specific cost which is described in detail in Azure's pricing page.
There's no nesting of separate services. In your specific case: there's no concept of creating an App Service inside a Virtual Machine (nor is there any hint of that anywhere). They are two separate services.