Building a scalable web application using Azure App Service and YugabyteDB allows developers to leverage cloud infrastructure and build more reliable and available applications. The process begins by deploying an eCommerce dashboard application, YB Shoes, which connects to a Node.js server that queries data from YugabyteDB Managed. To get started with Azure App Service, create a new web app using Node.js, deploy the application from a local repository, and configure settings such as continuous deployment and GitHub Actions. Deploying a database cluster on YugabyteDB Managed involves creating a cluster in the cloud, adding outbound addresses for the web app, seeding the cluster with data, and configuring Azure App Service settings. Finally, deploy the YB Shoes application to Azure using the Azure CLI or Visual Studio Code extension, configure the application settings, build and publish the application, and view it running in the Azure cloud infrastructure.