Which way is the enemy's gate? Why is this important?
The enemy's gate is "down." This of course refers to the Battle Room at Battle School and a tactical approach to re-orienting all soldiers so they have a common goal and a common sense of direction in a cubical room which contains no gravity.
While at Battle School, Ender quickly realizes that most commanders rely on the direction of gravity as it was in the corridor when they enter the Battle Room. This means that most of the time the enemy gate is directly "in front" of their gate. What Ender proposes when he instructs his army to imagine the enemy as "down" is genius. First, they immediately "drop in" on the enemy, presenting only their feet as moving targets, which are very small and hard to hit. Second, and most important for later, this "dropping in" on the enemy simulates the attack of a planet from space. No matter what part of the planet his army would "land on" they would all have to move "downward" to reach it. This proves to be the exact solution to the final battle on The Simulator when Ender is at Command School.
The enemy's gate is down. This actually becomes a rather iconic phrase from the novel. Ender advises his army to always associate the enemy's gate as below them in the simulated battles. The enemy's gate is what the army has to infiltrate to win the battle. By always associating the enemy's gate with down, Ender's army is able to cohesively win no matter what the gravity orientation is.