Apple has established a replacement program for some 3 TB hard drives in 27-inch iMacs sold between December 2012 and September 2013. These drives may fail under certain conditions. The program covers affected iMacs until 19 December 2015 or until the third anniversary of the original sales date, whichever period is longer.
You can enter your to see if it qualifies. If it does, you can get a free replacement at an Apple retail store or an Apple Authorized Service Provider. Apple also says it will reimburse anyone who has already paid for repair or replacement.
Before you have your iMac repaired, be sure to back up your data, preferably twice! If you don’t know where to start, check out Joe Kissell’s new “.” This isn’t just a precaution; once you get your iMac back, you’ll need to restore your data from backup.