There are a number of reasons why you are experiencing this issue, ranging from a simple software issue, like a corrupt file (unlikely), a corrupted sector of your Hard Drive or SSD (unlikely but not unheard of), to blocked air vents causing the system to overheat whilst trying to power the internal display (unlikely but possible), to the more complex, graphics card failure (unlikely if it works via HDMI without issue), possible logic board issue, moving on to a screen (or screen connecting ribbon / other screen related part) replacement, either of which requires Apple Technical Support for the repair.
To start with, restart your Mac in Safe Mode, using the instructions here (basically hold down the Shift key when you power on before the start up chime sounds):
Use safe mode to isolate issues with your Mac - Apple Support
Safe Mode loads only the basic 'essentials' for you Mac to operate. If it starts up and the screen is working fine, use the machine in safe mode for a while and see if the issue surfaces.
Launch Disk Utility (Applications > Utilities > Disk Utility), select your internal Hard Drive (on the left panel). Look at the Option Buttons along the top of the Right Hand Part of the Window and select First Aid. Select Run, Confirm the pausing of the internal Hard Drive (Select Run / Confirm) and let Disk Utility do it's thing. If any issues are discovered, follow the instructions to repair them. Once complete, Click Done, exit Disk Utility and restart your Mac.
If it doesn't, it would suggest a software related issue. Have you installed any new software or applied recent updates for anything before this issue started? Perhaps a program you are running has not been updated to work with Retina displays properly.
If so, try removing the software then restart you Mac as normal from safe mode.
When Restarting, hold down these four keys before the start up chime sounds:
cmd + R + P + alt (I use my left hand thumb and index finger for cmd (left of space bar) + R and my right hand thumb and index finger for alt (right hand side of space bar) + P. This will reset your PRAM.
When holding the four keys down, the start up chime will sound, keep holding them down. The system will restart and a second (usually louder) start up chime sound will be heard, release the four keys and allow your Mac to start as usual.
If your Mac runs as expected (with no display issue), you could try installing the offending update or software again and see if the display issue resurfaces. If so, repeat the above steps to remove the software once again and avoid that particular software until a new version or update to fix this issue is released. Contact the developer and report the issue to them.
If none of this works, then you will have to have an Apple authorised service engineer diagnose the issue for you.
I know it is unsettling when things do go wrong, but electronics, components etc. do go wrong or fail. It just happens and can happen even if you are very careful with your devices.
I hope this helps (if nothing else, if you try the safe boot method, it will prepare you for a potentially expensive repair.
I found this at iFixit discussion forums, while not the same issue, does involve vertical line related issues. If you click the View Answer option below the original post, it describes some of the possible causes and the only real solution.
SOLVED: Vertical line problem on retina screen - MacBook Pro 13" Retina Display Late 2013 - iFixit
Let us know how it goes.