Time Machine could not create a local snapshot to back up from.
Does anyone know what this means? I can't backup my MacBook Air using and external drive.
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Please refer to the following Discussion: HELP Time Machine won't back up after… - Apple Community
Unfortunately I do not know if it led to a resolution. Perhaps its most salient point is to run Disk Utility's First Aid on the source volume. You have to boot macOS Recovery for it to actually "repair" anything that needs repair: Start up from macOS Recovery, then follow the instructions in How to repair a Mac disk with Disk Utility - Apple Support.
In the end you may need to Contact Support because the inability to create a Local Snapshot is a show-stopper for which I do not have a solution other than the above.