Azure Functions is a FaaS service built atop App Service. It's an event-driven "serverless" computing platform that allows you to run code based on any number of triggers, such as HTTP requests, storage operations or orchestration events elsewhere in Azure.
Installing the Functions SDK
To develop and locally test Function Apps you'll need to install both a development environment for your chosen language and the Azure Functions SDK. The SDK enables you to run your Function App locally and allows you to publish your App to Azure.
For details of how to install the appropriate tools, see Microsoft's documentation.
Azure Functions are hosted on App Service plans.