The two circles represent two different companies. When the malware infects a system within these companies a coloured blog turns red.
Each company works in slightly different ways. The settings screen that appears at the beginning of the video shows how they differ. You can see how the differences affect the spread of the worm.
In this example I've set the simulator to show the effects the Melissa worm could have. You should notice that one company (Corporation 2) becomes completely infected much faster than the other.
Read about (and visualise) more viruses and other threats.