Connecting a GitHub repository to a Microsoft Azure instance streamlines the process of continuous deployment for web apps, allowing developers to efficiently push critical bug fixes and new features. This setup can be completed in under 10 minutes, requiring an existing Azure web app instance. Once the app is running, users can configure continuous deployment by linking the app to a specific GitHub repository and branch, typically the master branch, facilitating automatic deployment of any changes. This integration ensures that updates are live on the internet immediately after merging pull requests into the designated branch, thereby enhancing development productivity and focusing efforts on delivering quality code. Additional resources, such as video tutorials and detailed documentation, are available for further guidance on this process.