The backend is the software running on a server somewhere, the frontend is the website which people at home uses to interact with the software on the server.
So a full-stack programmer works on both server-side and client-side software, and the reason why this is important is that they use different technologies.
Frontend is CSS, HTML and JavaScript in some format, backend can be a lot of things like C# or any of the other languages built to do stuff server-side.