It's possible your startup volume is full or the disk drive has become corrupted or failed. If the drive is full then you have no other recourse but to erase the drive and install OS X from scratch. If the drive is corrupted then this will also fix that problem. If the drive has failed, then you will not be able to complete the task.
Install or Reinstall OS X from Scratch
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.
Erase the hard drive:
1. Select Disk Utility from the main menu and click on the Continue button.
2. After DU loads select your startup volume (usually Macintosh HD) from the
left side list. Click on the Erase tab in the DU main window.
3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on
the Security button and set the Zero Data option to one-pass. Click on
the Erase button and wait until the process has completed.
4. Quit DU and return to the main menu.
Reinstall OS X: Select Reinstall OS X and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible
because it is three times faster than wireless.
This should install the version of OS X that you had installed.