Your current prestige rating is displayed in the lord info panel.
Prestige can be earned by completing prestige quests.
Each day you may claim multiple rewards from the Prestige Quest panel, up to your current prestige rating. The higher your prestige rating, the more rewards you may collect each day.
Your prestige rating also affects which rare heroes are available to randomly appear in the tavern, the higher your rating, the higher quality rare heroes are available.