I have 2 directories on my GitHub repository. I'd like to delete one of them. How could I do that without deleting and re-creating entire repository?
You could checkout 'master' with both directories;
git rm -r one-of-the-directories // This deletes from filesystem
git commit . -m "Remove duplicated directory"
git push origin <your-git-branch> (typically 'master', but not always)
As mentioned in the comments, what you usually want to do is remove this directory from git but not delete it entirely from the filesystem (local)
In that case use:
git rm -r --cached myFolder