Git: A piece of software that keeps track of the entire history of things that you're working on on the computer, so you don't have to keep track of separate files and the history of the files manually. Git also allows people to collaborate on a single file.
Github: Is a web service where you can sign up, make an account and do Git stuff on a website. Github basically runs the git software behind the scenes and is a social network for projects that are managed through Git.
Repo: Is a project that can have multiple projects associated with it.
Commit: To save what you worked on.