What does this red icon on my panel mean?

It's letting you know that the package system is in a broken state (eg. some of the packages are in a broken state). You can try to resolve this by running the following command in a terminal.

sudo apt-get -f install

I got this same red and white warning icon and identical error code after having tried to install the wrong package accidentally (i386 on amd64 - Ubuntu 12.04 LTS) To resolve I...

1. ran dpkg --get-selections > ~/Desktop/packages in terminal to get a list of installed packages
2. removed the package that I had just tried to install using the name of the package as appearing in the above list and this command sudo apt-get purge name-of-package-here
3. ran the command above sudo apt-get -f install thanks tgm4883
4. removed some redundant packages with sudo apt-get autoremove (the suggestion appeared in terminal after running the prior command.) Either here or the command before resulted in the warning/error disappearing
5. I then ran sudo apt-get update which took much longer than usual and everything seems to be back to normal.