Which package update(s) triggered the 'Server reboot required' message?

One way to identify this info is to look in /var/run at these files

$ cat /var/run/reboot-required
*** System restart required ***
$ cat /var/run/reboot-required.pkgs
linux-base
linux-image-4.4.0-93-generic

These files will not exist unless a reboot is required, so checking if they exist is also a nice trick to know if a reboot is required:

[ -e /var/run/reboot-required* ] && echo "Reboot is required!" || echo "Reboot is not required."