Serverless computing, a model where providers manage servers, allows developers to concentrate on application logic and has gained popularity due to its auto-scaling capabilities, freeing them from server resource allocation tasks. This model integrates well into both traditional and microservice architectures, with major cloud providers offering their own serverless solutions, such as AWS, Google, and Azure. The tutorial guides users through the process of continuously deploying an Azure function using CircleCI, starting with prerequisite installations like Node.js and Azure CLI, creating an Azure Service Principal, and setting up a local Azure functions project. It proceeds with instructions on creating a storage account and an Azure function application, followed by automation of the deployment process using CircleCI by setting up environment variables and writing a deployment configuration in a config.yml file. The tutorial concludes by showcasing the benefits of serverless architectures, emphasizing their scalability and cost-effectiveness, and encouraging the integration of serverless functions into application processes.