Git is a free and open source distributed version control system designed by Linus Torvalds in 2005 to handle everything from small to large projects with speed and efficiency. It allows for tracking changes to code, collaborative work, and reverting to previous versions of code. GitHub is a site for hosting Git repositories online that adds features like documentation, bug tracking, and code review via pull requests. Common Git commands include git init to initialize a repository, git add to stage changes, git commit to save changes to the project history, and git push to upload changes to a remote repository.