It's like Reputation from WoW. Complete quests that help the Gargoyle Queen, gain Loyalty Rating. Kill monsters and enemies of the Gargoyle Queen, gain Loyalty Rating. The more Loyalty Rating you get, the more quests/items/areas/stuff you are allowed by her to access.
If you go around committing gargoyle genocide, you probably lose Loyalty, but I'm not entirely sure, as last time I checked, this system wasn't entirely implemented.