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You need to run Disk Utility by booting into OS X Recovery Mode.
Make sure the Mac is off .Hold down the Command and R keys, and power the Mac back up again.
Eventually, you'll end up on a screen headlined OS X Utilities. (Once you see that screen, you can release the keys you were holding down.) Click on Disk Utility. Then click on your Mac's built-in hard drive in the left column of Disk Utility. (Usually, you'll see two listings for your built-in drive: the first includes the drive's size, like 500GB, in its name; and nested underneath it is your drive's friendlier name. You want that second one.) On the lower right of the Disk Utility window, click Verify Disk, and then wait while Disk Utility does its thing.
If disk utility does not recover it then try opening your mac in safe mode :-
Shut the Mac down, and start it up while holding down Shift. Safe Boot can take a while if it does indeed work.
Be patient during your Safe Boot. If the Mac does start up, restart it from the Applemenu once the desktop finishes loading completely.
I will be back in sometime till then try both the above mentioned steps and follow instruction as mentioned above.
Once done try restarting your mac normally and let me know if you are still facing this issue.
Alright !! Thanks ..Sure take a look and let me know in case of any problem.
Once OS X is booted again, it can be a good idea to confirm all is well by going back to Disk Utility and running the “Verify” tool to check on the drives health.
Keep in mind that if the ‘fsck’ tool continuously fails or reports errors and Disk Utility is a no go as well, the hard drive itself very well may be failing and on its last legs, so be sure to initiate a back up all of your critical data using Time Machine or your backup method of choice, and aim to get the drive replaced sooner than later.
Even after that if you get the same error message Continuously "the mac hd could not be verified full" then try following :-
You have to run fsck from Single User Mode, recovery mode, or a separate boot partition, otherwise the drive is mounted in write mode and fsck can not work or run properly.
Reboot > hold down OPTION key> choose Recovery mode > go to Utilities menu > Terminal > then run fsck -fy command from there
The drive has to be reformatted and the system reinstalled. Do you have a backup?