A Full Stack Web Developer handles both front-end and back-end development of a website. They work on the user interface, design, and functionality (front-end), ensuring the site is user-friendly and visually appealing. On the back-end, they manage server data and requests, ensuring the website runs smoothly and efficiently. They are proficient in various programming languages like JavaScript, HTML, CSS for front-end and Python, Ruby, Java for back-end. They also work with databases and servers, and use version control systems. Essentially, they have the capabilities to build, test, and deploy complete web applications from scratch.