Obedience is a location in the northern section of the Fog Islands. As you approach Obedience, the area becomes much darker. It appears to be situated in a massive quarry, which still has scaffolding that stands to this day. If you're traveling with a Skeleton, he will remark that it was the obedience of his race to the humans that led them here to their destruction. Around the "lake" of what seems like ice, you may find gigantic skeleton heads and their upper bodies.
Aside from that, Obedience serves no purpose besides lore. It's a poetic little place to visit, especially with a Skeleton in your party. The fertility rates in Obedience are 0% for Arid and Green, but that's to be expected from a cryogenic bath. There are also no resources like iron or copper available. In short, don't go there expecting profit. Go there for the experience or the detour into Mongrel/the North.
Background Lore (may contain spoilers):
It is implied that when the humans became fearful or had no use for their creations, they marched the skeletons into a quarry they dug for themselves. Afterwards, the humans (or perhaps skeletons under their command?) filled it with some sort of chemical agent, ultimately "killing" or destroying/freezing most of them where they stood. This theory of the use of chemicals is reinforced by the thick white fog that surrounds Obedience and the islands, as well as the hazardous atmosphere that forces people to wear masks. Likely it was similar to a cryogenic compound or liquid hydrogen, which gave off a deadly gas as time went on.