Sometimes the package installation or upgrading process can be broken for some reasons.
In cases like that DO NOT reboot your system, try to fix it before rebooting.
If you already rebooted the system and you cannot log back in to your account, reboot it again and run the system in Recovery Mode.
Every command has to be run with root privileges su or sudo.
Fix broken packages via dpkg tool - it will install all already downloaded packages:
dpkg --configure -a
Sometimes broken packages need more (missing) dependencies, so dpkg can't solve that. Use apt-get to fix everything what is not properly configured yet and needs some new packages to be downloaded:
apt-get update apt-get install -f
If you just fixed some packages after broken upgrading process, run upgrade again, to make sure that there is nothing left to be upgraded/fixed again: