GitHub is a platform for the code hosting and collaborative development based on DVCS (Distributed Version Control System) Git. It's a fusion of a social network and a file repository and it offers subscription hosting plans, for private software projects, and free, for open source software projects.
It is now the most common and used platform for collaborative development and it's used where it's required a continuous update and storage of development projects managed by team of 2 or more people. GitHub is perfect for collaborating with colleagues from different offices to any kind of documents and reports.
Git is a system for single people or even big teams for managing source code changes. The software keep traces of every code change made, in order to have all the revisions and to access to the previous versions.