Win Battles in the Battle Page to earn Battle Points. Opponent's rank determines how many Battle Points you will gain or lose. The higher your opponent's rank relative to yours, the more points you gain for winning. Losing battles will subtract Battle Points from you.
You can move down in Ranks, but never in Tiers. Great rare rewards for achieving tiers are unlocked for purchase in the Soldiers, Blacksmith and Magic page upon achieving ranks. Check out the page Battle Rank for more information.