There are several tutorials online for github. This is mine.
GitHub is a version control system. In simpler words, GitHub provides a huge storage for developers, bussiness companies to store, add, edit their files.
GitHub is nowadays used for storing programmes of any individual or any organizations. It's free and open source. Though they provide private repo for many prices.
Respository is the area where your works will be saved in GitHub.
Suppose you like a project and wanna contribute on that, so you make changes to a file or files then give the project a pull request.
Pull request is just a request to the owner of that project to pull your code to his/her project ( You are requesting to project owner " please pull my code and merge it .") .