What is the third invasion?

The third invasion involves all human ships being sent out to attack the buggers. Ender questions why they are fighting the buggers, and although Graff does not know, he speculates that a species that can communicate through thought must have a hard time understanding that humans are intelligent life at all. So it could all just be a misunderstanding, but when the species is at stake, there is no choice but to attack.

The Third Invasion is in fact really the first invasion, for the humans, that is. The First and Second Invasions were by the Bugger's (or Formics) attacking the Earth, but the Third was the humans (commanded by Ender) attacking the Bugger worlds. The Third Invasion was eventually called the War of Xenocide (destruction of alien species), and Ender became known as the great Xenocide.