User testing (also called usability testing) is the process of having an unbiased party test a product to determine how easy the product is to use.
In the words of blog.testlodge.com, "The goal with Usability Testing is to recreate real world scenarios where the user will be actually using your product, then by observing their behavior you will be able to understand what could be done better."
Cross browser testing is the process of testing a website in different browsers to ensure the quality of the code in each browser. It helps to make sure that no user will be unable to view the content due to the browser they're using.
Sources