Time machine back up error

Unfortunately, your backups are corrupted and are no longer useable. The Time Capsule hard drive needs to be erased and then you can start over again with new complete backup and move forward again.

Open AirPort Utility on your Mac (Finder > Applications > Utilities > AirPort Utility)

Click on the Time Capsule to select it, then click Edit in the smaller window that appears

Click the Disks tab at the top of the next window

Click Erase Disk

In the next window that appears, click the Quick Erase option

The erase will only take a few minutes, then you can wait for Time Machine to start a new backup. You may be asked to verify the Time Capsule disk before the backup will begin.

The corrupted backup issue tends to begin occurring in Time Capsules that are 7-8 years old or older. Once this issue occurs, it is likely that it will occur again. It's more a question of "when" and not "if".

So, if the Time Capsule is getting up there in age, I would not recommend that you keep data or backups on the Time Capsule that you cannot afford to lose.