Ah yes! Sorry about that. Seemed my question got lost in the conversation I had.

Lets start with some need to know things:
Each kingdom has a King. The king of that kingdom, is a game controlled figure head. He will issue orders to you (I assume in kingdom event format) at random (or not) times.

So on to the types of reputation:

Player with order -
Shows your reputation to your order.

Raise:
Participating in battles with your order will raise this.

Player with king -
Shows your reputation to each of the listed kingdoms.

Raise:
Complete tasks which are given to you by your king.
Fight players from another kingdom.

Kings with kings:
Shows you kingdom's reputation with the other listed kingdoms.

Raise: (for these next examples, I will list 3 kingdoms, A,S, and D)
A and S are allies which attack D in a joint attack.
A and S are enemies and D attacks S. A and D will get a rep up.

Lower:
Fight players from other kingdom.