Azure WebJobs is a great way for running any kind of script or executable as a background process in connection with an App Service Web App. You can upload an executable or script as a WebJob and run it either on a schedule or continuously. The WebJob can perform any function you can stick into a command line script or program and using the Azure WebJobs SDK, you can trigger actions to happen as a result of inputs from a Azure Queues, Blobs, Azure Service Bus, and much more.
WebHooks provide a simple mechanism for sending event notification across web applications and external services. For example, you can receive a WebHook when someone sends money to your PayPal account, or when a message is posted to Slack, or a picture is posted to Instagram.
The blog Sending ASP.NET WebHooks from Azure WebJobs describes how to send ASP.NET WebHooks from Azure WebJobs triggered by anything that can kick off a WebJob.