What lesson does Ender learn from his battle with Rabbit Army?

Ender learns a lot of important lessons from his battle with Rabbit Army. Some of them are small lessons, but none of them are unimportant to Ender. That's what makes Ender so dangerous. He can take seemingly innocuous information and find great meaning and value in it. It's why he wins over and over again. We can see this right away when the battle begins and Rabbit Army spills out and takes up formation. Ender has only been working with his new tactics for four weeks. Seeing Rabbit Army do the predictable helps him learn that his new tactics are far better than existing thinking.

Even with less than four weeks together, the way they fought already seemed like the only intelligent way, the only possible way. Ender was almost surprised that Rabbit Army didn't know already that they were hopelessly out of date.

Ender also learns that Crazy Tom is an effective leader within Dragon Army.

Crazy Tom, the leader of C toon, had apparently ordered his men to flash their own legs already. It was a pretty good idea in this dim light, since the lighted flash suits went dark wherever they were frozen.

Ender's army wins the battle, so he does learn that his new and creative tactics are effective. Ender also learns a valuable lesson in humility and dignity from the way that Carn Carby accepts his defeat.

I will remember this, thought Ender, when I am defeated. To keep dignity, and give honor where it's due, so that defeat is not disgrace. And I hope I don't have to do it often.

In Orson Scott Card's novel Ender's Game, a young Ender is made commander of the Dragon Army, a small group of fellow military students. Ender's army is forced to battle the Rabbit Army—a group known to be more good-natured than others. Despite having to battle months earlier than expected, the Dragon Army crushes the Rabbit Army. This leads to Ender being shunned by the other army leaders, as they are shocked by and jealous of his early success. Through his success, Ender learns two key things: that his continued domination as both student and commander will lead always lead to him being an outsider and that his unique army maneuvers (having five flexible toons) are successful. However, he also learns he can find a friend in Carn Carby, the Rabbit Army leader.