Before we talk about GitHub, we need to get a basic understanding of what git is. Git is a free and open source version control system. There are many different types of version control systems that all do basically the same thing; they create save points for any project that you are working on. A version control system allows a user to track additions, deletions, and edits to your project. Think of a version control system as a big picture book with every page a different save point. Every page of this book builds off the last page, they look the same but have changes to the picture and new things have popped up in the picture. Not only that but the book also tell you what has changed from one page to the next, somewhat like those spot the differences pictures but this has everything circled for you so its easy to find. That is git.
Now that we know about git, we need to learn about GitHub and the difference between that and git. Git is a version control system but think of it as only working on your computer, its local. GitHub is a version control system but it is connected to online servers, its global. Github can be accessed from your computer or any other computer from around the work. This allows multiple users to work on the same project. Lets go back to the book analogy. Git would be like a hard copy of a book you keep at home, you have control of all the pages and what is added, edited, deleted. GitHub is an ebook. Anyone that you allow to can read the story, add, edit and delete anything they want. Any changes made also affects all the other ebooks.
There are two main reasons I think people should use GitHub. The first we already stated, you can work on projects with multiple people around the work. The other reason is security. Your files are back up in multiple places, not just on your local computer. If something happens to your computer, the files are still safe. If you lost the only hard copy of the book its lost forever, but with an ebook you can always download it again. Not only that but the security of having save points to a project. At any point you can revert back to a previous point in the project. If something breaks or you don't like it, you can go to a previous save point and undo the changes. Lets say you have been working on the book and you have tons of changes. You see that some changes have ruined the story, but thats okay because we can just go back to a previous page and change how the story will end.
Hopefully this gives you a better understand of what a version control system is and why you should use GitHub.