The 'This branch is out-of-date' warning in GitHub pull requests signifies that your feature branch doesn’t have the latest commits from the base branch, often `main` or `master`. To fix this, go to your local repository and pull the latest changes from the base branch with `git pull origin main` (replace `main` with the relevant branch name). After pulling, you have two options to integrate these updates: merge or rebase. A merge is straightforward, where you can use `git merge main` to bring the base branch changes into your feature branch, followed by committing the merge. Alternatively, you can rebase with `git rebase main`, which places your commits on top of the latest base branch commits, creating a cleaner history. Once you’ve updated your branch locally, push it to GitHub, and the 'out-of-date' warning should disappear. This approach keeps your pull request compatible with the latest code on the base branch, making integration smoother.