This is caused by a consistency error on the partition containing the root file system. It is often triggered by improperly shutting down the machine.
The general fix is:
# 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.
# 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.
https://askubuntu.com/questions/885062/root-file-system-requires-manual-fsck