You know when I said, create your own branch for your own changes before adding anything?
What you are doing is 'tracking' the MOODLE_27_STABLE branch on Moodle's remote git repository. You have then changed something and committed it. If you had write access to that site, pushing it would change core Moodle (!!). You don't - which is just as well
This is why you would first create and switch to (git checkout -b myownbranch) your own branch before making any local changes.
What you could do as well is to get your own Github account and then push your branch there. This gives you a backup.