GitHub is a web-based hosting service for software development projects that use the Git revision control system
Git is a distributed revision control system created by none other than Linus Torvalds. The beauty of Git lies in its distributed nature which is different from other traditional revision control systems. Git gives each developer a local copy of the entire development history, and changes are copied from one such repository to another. These changes are imported as additional development branches, and can be merged in the same way as a locally developed branch. The distributed nature of Git also requires that code by merged much often that other systems and for that reason much of the implementation of Git has is in C programming language. In this video of Linus Torvalds at Google, he talks about how easy it is to merge thousands of lines of code in Git.
Coming back to Github, it provides social networking functionality such as feeds, followers and the network graph to display how developers work on their versions of a repository. Users can also create wikis for individual repositories and static web pages which can served by static web site generator Jekyll. Infact the source of the site you are viewing right now is hosted on Github repository.