Are you able to talk about how the battles actually work?
Sure. Take a look at the screenshots of battles in this and Fletcher's AAR.
You have leader strengths, which effect each side. Hannibal has special battle tactics (cards).
You choose up to 8 units to man the front line of each round of battle. Cavalry is useful in the frontline in case the enemy tries to retreat, in which case your cavalry can pursue (their cavalry can screen the pursuit).
There are elephants, calvalry, archers, infantry, etc., all with unique attack and defense strengths, and some with attack bonuses.
Each round the sides have a chance to inflict hits and routs. Some routed units can be returned to battle, at the expense of leader strength. Others, like Gallic units can not return after being routed, except if Hannibal plays some tactics.
There are field battles, sieges, storming of cities, attacks against enemy encampments, naval battles.