Fork makes a copy of a repository to your Github account. This can be used so you can make changes without changing the original repository. Once you are done with your changes, you can request to have the fork merged back with the original code.
Clone makes a copy of a repository on your local computer. This is similar to fork, as you can make changes and later have them merged with the original code. You can also have changes to the original repository be added to your clone.
Branch makes a new branch for a repository. Originally, there is one branch where everything resides, but creating a new branch allows you to make changes without affecting the original repository. Of course, this can be merged later with the original. This exists at the same place as the original repository, whereas a fork and clone do not.
I believe the difference between clone and fork is that clone makes a copy to your local computer, whereas fork simply makes a copy on Github. I believe branches are different in that they are not copied to your account or local computer, but exist as a separate part of the original repository.