Azure Functions is a compute service created by Microsoft that can execute Python code in response to pre-defined events, such as API calls or database transactions in other Azure services.
An introduction to Azure Functions is the official quickstart guide by Microsoft and has some good high-level information on their platform's services as well.
Deploy Python to Azure Functions provides the step-by-step instructions needed to get Python code running on Azure Functions.
Azure Functions vs AWS Lambda – Scaling Face Off contains metrics from comparing AWS Lambda with Azure Functions in response time, user load, requests per second and error rate over various periods of time.
How to build a serverless report server with Azure Functions and SendGrid combines the Sendgrid email API with some configuration code to have Azure Functions kick off email jobs.
azure-cli are the command line tools for using all of Azure, not just Functions.
My (Rough) Start with Azure Functions painstakingly details signing up for Azure, accessing Functions and finally coding a Function. The author has some really great points on what is confusing to newcomers that hopefully will be addressed as Microsoft continues to work on their Azure platform.
Azure in Plain English covers all of the Azure services and explains them because their default names are often too vague to understand their purpose.