The favor system of the Rose Of Eternity is essentially an extension of the current quest system.  It works like so...

	Complete a quest for a particular NPC.
	NPC will favor you more (you will get a confirmation in your journal)
	Later, after some events have occurred, the NPC will either give you another quest, or possibly give you a special item.

Here is a brief example of a simple favor quest...

1. There will be a Father who is looking for his son.  You accept quest to find him.
2. Once you find the son, you can either turn him in to his Father, or accept a bribe from the son and not say anything.
3. If you turn the son into his Father, you will receive experience points.
4. If you accept the bribe from the kid, you will get the item the kid bribes you with.  In addition (this is where the favor system comes in) he will favor you.  Now, at that point, it means nothing.  Later however, this kid will remember what you did for him, and give you a special item. 
5. That in a nutshell is the simplest example of a favor quest from The Rose Of Eternity.