Unfortunately, that screen indicates that either the system files are corrupted or the hard drive has failed suddenly. You’ll likely need to take it in to get it replaced. But before I send you out to do that, let’s check every possibility to be sure it isn’t something else in an effort to save you from that expensive repair.
We can run Disk Utility and see if it works or not. Turn off your Mac by holding down Power button for 10 seconds. Then turn it back on and immediately hold down Command and R keys at same time for 20 seconds and this will boot your Mac to the Mac OS X Utilities screen. From there, click Disk Utility. Select your hard disk at left column (Macintosh HD or hard disk name). Then click Verify Disk (under First Aid). If asked to repair, click Repair Disk. Then click Repair Permission.
If you are using latest Mac OS X El Capitan, then you will not see Repair Disk option in Disk Utility. Instead click First Aid button and run it. Repair if asked.
Then restart from Apple menu. If that didn't work, then turn it off. Turn it back on and immediately hold down Command, Option, P and R keys at the same time for5seconds, then release the keys and immediately hold down Shift key for20seconds. Does it boot into desktop ?
Please let me know if that didn't work, so we can continue troubleshooting.
Note : Since your Mac is not loading the OS X, I will not be able to connect to your Mac and fix it from here. So please ignore/close the secure remote assistance message you get from here and don't accept it yet. I will send you instructions in here.