My Raspberry Pi 3 Model B outputs the following when trying to initially boot:
Kernel panic-not syncing: VFS: unable to mount root fs on unknown- block(179,2)
After rebooting, I still receive the same error. The Pi is unable to "shift boot" to do a filesystem check and repair. This is a new installation without ever going through installation or setup.
Previously I had Ubuntu MATE installed on this SDHC 16GB card. During that installation, I had problems with formatting the filesystem(ext4), memory build up, half of the memory being completely unusable, and slow and jittery graphics. After turning off the compositors but still using the Marco WM, I still saw the same graphics errors.
After confirming to switch to a different Operating System, I (successfully?) installed Raspbian (wanting a more Debian based environment) on Mac OS X with:
sudo dd if=sudo dd if=/Users/[username]/Downloads/2016-05-27-raspbian-jessie.img of=/dev/disk1 bs=1m count=1024
with [username] being my username of course.
I have no idea whether any of this is useful in effectively diagnosing and correcting this error, but I am still willing to add any info if someone asks in the comments.