I have a Github repository that I forked from some other project several months ago. It is now several months later and the original master repo has changed. I would like to update my repo to reflect those changes. Is this possible in the Github web interface? Or do I just need to delete the repo and re-fork it?
You can try and reverse how pull requests happen.
If your code somehow conflicts or is not quite clean enough, then this will not work to update via the GitHub web interface and you will need grab the code and resolve any conflicts on your machine before pushing back to your fork.