Perform Repair Permissions & Repair Disk from Disk Utility on the main drive, but do it booted to your Recovery Partition. Boot, while holding down the OPTION key, until you are given a choice of boot disks. Choose the Recovery drive, then run Disk Utility.
If that does not alleviate the problem, perform a Repair Installation of OS X, again from the Recovery Partition.
Let me explain.
You can't ask a drive partition to "repair itself".
So, you have to be booted to a different drive, than the drive that is causing the problem.
In this case, your problem disk is your startup disk. The "startup disk" is the drive that you boot to every day. So in this case, we need to boot to a different disk. On your system, you have the main startup drive on one partiton, and the Recovery Disk on a separate partition. Both of these partitions physically reside on your computer's hard drive, or SSD, but appear to be two independent drives to the system.
You are going to boot to the Recovery Disk, or more accurately sometimes called, the "Recovery Partition". To do this, we use the "option boot". This means holding down the OPTION key, while booting. After a few moments, you will be presented by a display of avaialble boot disks. You choose the one marked "recovery". Once booted up, you will chose Disk Utility. This is an App that is built-in to the Recovery Partiton for the sole purpose of managing drives, disks, and partitions without having to be booted to the main startup disk.
From here, you can select the starup drive, usually called "Macintosh HD", by default. After you select the drive, you can perform actions on that drive. One button will "repair permissions", another will "verify disk", and still another with "repair disk". By running "repair disk", Disk utility will attempt to repair certain software errors on the drive that might be preventing a good read of critical files needed to boot to the startup drive.
As well, "Repair Permissions" can also fix certain problems that may make the system unusable, or difficult.
You can also exit Disk Utility to perform a reinstalltion of the operating system, or recovery from a Time Machine backup.
As a last ditch, you can use disk Utility to completely erase your startup disk, in preparation for reinstallation of the OS. (this is after ALL ELSE fails)