From the wiki:
Respect is a hard-earned value which determines whether your servants see you as a worthy leader or just as the person who happens to be hiring or owning them. It is most readily increased in NPCs if they are with you in a fight in which you successfully defeat enemies. Successfully managing certain dangerous events might also increase Respect. As can just talking with NPCs.
Certain rare events might lower Respect, but it's a stable value that doesn't naturally change over time.
Respect boosts all Domination and Charm attempts. An NPC is more likely to participate in sexual intercourse or do as you command (even if they don't like it) if their Respect for you is high.
How to increase Respect
- Through combat encounters, per battle won. 100% chance of +1, up to a value of 20, then 7% chance of +1, up to a cap of 50.
- Through certain domestic events, including talking to an NPC and asking them how they are. This can produce a variety of effects, one of them being increasing their respect for you by 1 point (smallish chance).
- Through certain quest events tied to a specific NPC.