Okay, I believe your screen looks similar to this:
Note the long string in the red box that is next to Logical Volume Group with the name Macintosh HD. This is called the UUID. It appears yours is as follows but verify that:
diskutil CoreStorage delete UUID
(where "UUID" is replaced with the string you identified)
and press enter/return.
Once the CoreStorage volume has been deleted, you should be able to return to Disk Utility and format the hard drive. You may or may not have to restart the system and return to the Recovery HD partition first (Command-R at startup).
In Disk Utility, select your normal, physical hard drive from the list in the sidebar and then choose the "Partition" tab.
Under Volume Scheme, click "Current" and choose "1 Partition".
Name your hard drive on the right side (usually "Macintosh HD") and choose "Mac OS Extended (Journaled)" as the format.
Click options and verify GUID partition table is selected and click OK.
Now click Apply.
Once the process has completed, exit Disk Utility.
Then, try installing OS X.