Well, there is a couple different reputations and the biggest of them is the Reputations Rating. Also added a separate page with all the requirements for Worship Badges or a more convinent and quicker overlook.
Then you have City Reputation which decides what kind of Summons and Bags you can buy [general speaking].
There is also a Clan Reputation, which helps your Clan in rankings and you can buy Banners to help yourself and your clannies in Fights.
And last we have Trophy Hunters, which could be seen as a Reputation for those that are all for PvP fights.