Each Maori Thing increases your Fervor when Summoned. Unlike Resources, Mana, and Acquires, Fervor does not reset at the end of your turn. This allows you to build up Fervor over subsequent turns. However, at the end of your turn, your Fervor is decreased by 1. So, if you don't Summon Things to keep building it up, it will drain away eventually.
During your Acquire phase, if you have the appropriate amount of Fervor, you can purchase Maori Objects.
Each of these objects provides you with Honor at the end of the game. In addition to providing Honor, you may also Summon these Things during your Summon phase for additional abilities.