"Full Assaults" by Terrorists: If you have made the terrorists mad, or if you are a big country, the Terrorist will launch a full assault on your country. They will declar war, and probably launch a series of missiles. This war last 48 revolutions, like all other wars. During this war, the country's members all get a +3 terrorist threat level.
Terrorist Messages: Terrorist will send you messages (death threats), to keep all the players on their toes. They are totally random, so dont be scared =)
Terrorists Attacks: If you threat level is 4 or above, you will be attacked at random times by terrorists. This can also include probe attempts.