The root filesystem on /dev/sda2 requires a manual fsck
# Replace <partition> with that specified in the error (e.g. /dev/sda2).
(initramfs) fsck <partition with error>
Enter Yes(y) to all prompts. Once complete, you will again be presented with the (initramfs) prompt.
# or use
fsck -yf /dev/sda2
# y in -yf is for yes wherever the system asks for y/n choice
# The -f is to force check a filesystem, even if it is seen as clean. More of a reflex,
# might not be required when your system refuses to boot on that partition
# Reboot the machine.
(initramfs) reboot
You may have an issue with package manager upon reboot. In this case:
$ sudo apt-get update && apt-get clean && apt-get update && apt-get upgrade
Members of the Ubuntu community using SSDs (solid state drives) have reported this problem numerous times; this points to a potential bug in Ubuntu.