The new browser matrix widget is a feature that provides detailed information about test runs on different platforms using Sauce Labs. It allows users to present their last build details in a more informative way, giving them and the community a fast look into the status of all tests runs made against various browsers and operating systems. The widget can be easily integrated into project pages by following simple steps, including choosing a corresponding Sauce account, running tests on that account's username and access key, setting build and pass/fail status for every test, and using a specific HTML snippet or Markdown code to display the widget.