What happened is for some reason OS X isn't booting, so it booted into Recovery (either Recovery HD partition or Internet Recovery if you saw a globe thingy)
So you use Disk Utility to repair/permissions on the Macintosh HD partition. Do not use it to Erase the Macintosh HD partition, that WILL erase your files.
The firmware might have just gotten the wrong partiiton to boot from messed up, hold the option key down ona wired or built in keyboard while booting the computer, see if you can boot the Macintosh HD partition with OS X, then set Startup Disk in System Preferences to remind the firmware which correct partition it's supposed to boot from.
Run through these list of fixes, or take your machine to someone who can.
..Step by Step to fix your Mac
Apple doesn't do data recovery, they will wipe your drive and blame you for not making a backup of your files, but a local PC/Mac repair shop can do data recovery before they wipe and intstall or fix your machine.
Most commonly used backup methods