The 'non-fast-forward' error on GitHub occurs because your branch is out of sync with the remote branch, meaning the remote branch has commits that your local branch doesn’t. This often happens when another collaborator has pushed changes to the branch you’re working on. To resolve this, start by using `git fetch` to bring the latest remote changes into your local repository. Then, you have two main options: merging or rebasing. To merge, use `git merge origin/branch-name` to combine the changes from the remote branch with yours, creating a new commit that reconciles both versions. If you prefer rebase, use `git rebase origin/branch-name` to apply your commits on top of the fetched commits, which keeps your history linear. Once your local branch is updated, you should be able to push without encountering a fast-forward error. Remember, if you are unsure about which approach to use, merging is generally safer as rebasing rewrites history, which can affect collaboration.