The 100-Egg Evacuation is an event that took place 6 years prior the beginning of the series.
Knowing that they wouldn't win a war against the humans, the elders and Shagotte decide to gather 100 Exceed eggs and let them escape into Earth Land. However, they decided to tell the Exceeds that it's a plan to destroy the monsters of the other world known as the Dragon Slayers in order to prevent a panic. Using the humans' anima, the plan succeeded. One-hundred Exceed eggs were taken from their parents and sent to Earth Land on a mission to eliminate the Dragon Slayers.
Once the unborn Exceeds arrived at Earth Land, they did not know of their "mission". The mission the Exceeds were given was later revealed to be a lie. Due to the Queen's power to see the future, she foresaw Extalia's destruction. So in order to keep the species alive, she sent 100 eggs, including her own, to Earth Land to protect them, and lied about the mission to kill the Dragon Slayers to the other Exceed.