Git is a revisionor version control system, a tool to manage your source code history.
In the SVN analogy, Git replaces SVN, while GitHub replaces SourceForge. So , essentially - GitHub is a hosting service for your Git repositories. And , most notably, GitHub is a consequence of the existence of git and not the only hosting service.
For folks who are new to GIT , this is an absolute awesome 15 min. refresher.