When you see 'This branch is out-of-date with the base branch' on GitHub, it means your branch is missing recent commits from the main or base branch, leading to potential conflicts if merged as-is. To resolve this, first update your branch by pulling the latest changes from the base branch, commonly the `main` or `master` branch. In your terminal, switch to your working branch with `git checkout your-branch`, then run `git pull origin main` (replace 'main' with the correct base branch). Alternatively, you can use `git rebase main` to reapply your commits on top of the updated base branch commits, helping maintain a cleaner commit history. After rebasing or merging, push your changes back to GitHub with `git push origin your-branch`, and your pull request should now be up-to-date. Remember that rebasing can cause conflicts, so carefully resolve any that arise. Once completed, GitHub should recognize your branch as current, allowing a smooth merge into the base branch without further issues.