There aren't many chances to encounter disk errors on Mac, but over the period, the file system might get corrupted and display disk errors. There is basic troubleshooting like restarting your Mac, to resolve these kinds of error. But if the problem is serious, you’ll need to repair these disk errors from Recovery Mode.
Chill, it isn't as scary as it sounds. You'll just need to get into the Recovery Mode on your Mac and then make few clicks here and there to get the job done. Anyways, we have mentioned a detailed process below for better understanding. Give it a look and you'll be just fine.
How to Repair Disk Using Recovery Mode on Mac
Step #1. Assuming that you are already in the Recovery Mode, click on Disk Utility and then click Continue.
Step #2. You'll get a sidebar with all the volumes. Select the one you wish to repair.
Step #3. After you have selected the volume to be repaired, click on the First Aid button.
Step #4. Now all you need to do is to click on Repair Disk.
After the process is completed, there are two possible options: either your disk will be termed as “OK” or you will be given either of the two errors.
If you get “overlapped extent allocation” error, then there can be two or more files having the same space on the disk, and possibly either of them is corrupted. Check each of the files in the list and decide, whether you can edit, re-create, or delete them.
Now if you get “The underlying task reported failure” error, then it means that the disk is not completely repaired. So perform Disk Repair once again and check if it is successfully completed. If it doesn't work, backup as much as you can, and format the volume, followed by re-installing your OS X.
If your disk is physically damaged, then there is no other option then to replace it.