Final answer:
To fix Time Machine backup issues, check preferences, consider changing backup volume permissions, or format the backup volume if necessary, and as a general troubleshooting step, reboot the computer. These actions can help to resolve errors related to file copying issues during backup.
Step-by-step explanation:
The issue of Time Machine failing to complete a backup can arise from various factors. When the alert message states, 'Unable to complete backup. An error occurred while copying files to the backup volume,' it suggests a possible problem with the backup volume itself or with the permissions. To address this, you can start by checking the Time Machine preferences to ensure that the backup is set up correctly. If the preferences seem alright, and the problem persists, you might need to format the backup volume, although this will erase any existing backups on the volume, so it should be your last resort. Another potential solution could be to change the backup volume permissions, ensuring that your macOS user account has the necessary rights to write to the Volume. While all these are valid troubleshooting steps, a sometimes overlooked but simple solution is to reboot the computer which can resolve temporary software glitches that could be preventing Time Machine from completing its backup process.