Drills are a way to train your commanders and improve your military performance.
They require Ammo and/or Supplies to activate and provide temporary boosts to your capabilities. However, these boosts decrease over time, so you need to keep running drills regularly to maintain their effect.
Drills are especially useful before important battles, as they give you that extra edge needed to win close fights.
Keeping your drills active ensures your military stays sharp and ready for combat.