What does it mean "Processing Triggers for..." after installing/Uninstalling?

Those are normal messages to get when dealing with packages, and are actually there to prevent you from having to take any actions. Without those triggers, you would have to logout/login or reboot for some changes to show up.

The reason they are there is to give other tools a chance to update - for instance, the list of applications in the unity dash would need to update to not show newly removed items. There are other triggers for man pages (documentation), grub bootloader (new kernel versions), and many others.

You don't need to do anything - these are informational messages so that you can monitor the progress of the (un)installation.