There should be a slew of tests performed on your website to make sure that everything works and that your users have a good experience.
Manual testing (often called user testing) is where the site is manually tested from the point of view of the user by actions such as clicking buttons, filling out forms, and testing that all the behind the scenes logic creates the intended user experience. This involves you loading up your webpage and checking that everything works as you intend it to.
Automated testing involves using scripts and a testing frameworks to test functionality automatically. Automated testing can be quick, thorough, and allow the developer to pick up errors early on but relies on the developer asking the right questions and does not test for user experience.
Furthermore, you should test how your website works across various browsers and devices, that your website meets all accessibility standards, performs well and does not take a long time to load, all of your written code is validated to the highest standards, and any major bugs you encounter are documented along with their fix to highlight your development process.