This indicates an error in the Linux kernel. The screen you see is supposed to serve the developer to figure out what went wrong. It is unlikely to happen again. In the case it happens you can reboot you computer with Ctrl+Alt+S-Abf+r, Ctrl+Alt+S-Abf+e, Ctrl+Alt+S-Abf+i, Ctrl+Alt+S-Abf+s, Ctrl+Alt+S-Abf+u,Ctrl+Alt+S-Abf+b.
After you booted the next time, run
sudo dpkg --configure -a and
sudo dkms autoinstall in a terminal to resume your update.
It's pure speculation whether the error is related to the updates or caused by the changes introduced without understanding, the latter is more likely, though. If the kernel crashed you can't do much more as a user than cross fingers that the journal of filesystem will recover correctly. Those crashes are not supposed to happen on the stable release versions of Ubuntu if they don't occur in third party kernel modules (e.g. dkms modules)! You can send a bug report to the linux kernel developers by following https://www.kernel.org/pub/linux/docs/lkml/reporting-bugs.html. The handling of the information on the screen you see it described on http://users.sosdg.org/~qiyong/lxr/source/Documentation/oops-tracing.txt in detail.
If you want to get started to understand and debug kernel crashes, start by learning to read the stack trace, how to use the Linux Magic System Request Key Hacks (I listed some of them without explanation above) and how to set up the kernel to produce more logging information (see https://www.kernel.org/doc/Documentation/sysrq.txt for details) so that you can reduce the cause for the crash step by step until a reproducable test case. Then you can create accurate issue reports on http://bugzilla.kernel.org or hack the kernel yourself and populate the patch.
See also What is kernel panic?.