I’m not sure how, but the first thing I ever saw of GitHub was their mascot, Octocat. Now it’s a face I, and many other developers, see quite regularly.
At its core, GitHub is a place where people share code & collaborate with others. It is currently the largest code host in the world. I personally have the Smart Web App Banner project I’ve written about on there, and contribute to ThinkUp among other projects.
GitHub also functions as a version control system, issue tracker, and discussion platform. I won’t go into too much detail, but these features are amazingly powerful on their own. Some projects have chosen to be private to protect their work & assets while enjoying these features.
Meanwhile, you will find countless projects that are 100% publicly visible (every line of code, every image, etc.), open to outside contributions, and allow people to fork their work to be customized in a way that someone else will be responsible for managing that version of that project (read more about forking here). Code merging can be done if the work done to a fork (big or small) is worth adding back to the main project.
If you’re a programmer, you should definitely browse & search through some of the great work on GitHub (some of these great tools come directly from Facebook, Twitter, etc.) Then you know that project you’re using is open to being improved by you whenever you happen to find a bug or want a new feature to be added. That freedom is valuable to have.