Attributes play a crucial role in HTML elements, providing additional information and changing their behavior based on scenarios or events. In Selenium automation testing, getting data of attributes can be super useful to test scenarios where just verifying text value is not enough. The `getAttribute()` method in Selenium is used to get attributes of HTML elements under test, returning the attribute value if present, or null otherwise. This method can be used to fetch values for different attributes like class, name, src, CSS style value, etc. By leveraging cloud-based Selenium Grids like LambdaTest, browser compatibility testing at a large scale can be performed, allowing automation tests to run across 2,000+ browsers and operating systems online.