The cages room caters to a couple basic fetishes: Zoophilia and pet training. Either or both. But generally all are welcome if they don't disrupt.
Let me speak first on pet training. There are many varieties and flavors (pony,dog,kitty,etc) but all are generally about a submissive person assuming the likeness of the animal and being trained by a Dom. Why would people want that? Well for myself it is because the relationship between a real pet and it's owner embodies many aspects of the sort of Dom/sub relationship I like. The pet is owned, but the relationship functions primarily on the desire of the pet to please and the ability of the Owner to foster the pets needs. The owner is completely dominant but a pet always chooses of it's own will to obey. Owners directly address dissatisfaction with pets through discipline. Pets always express their desires plainly and honestly. There is no judgment of either side.
In addition to the relationship paralleling the type I like there is an intense power exchange in the humiliation a human faces acting the part of an animal. The relationship provides for humiliation and physical abuse of the sub and as a Dom I feed on those as well. Dogs pee in public. Dogs fuck unabashedly. Trainers beat bad dogs. Dogs bite and scratch and claw. All sorts of fun things
Zoophilia is for me largely about degradation, abuse, and primal behavior. Animals are gentle when it comes to sex. Often that is something I want to incorporate.
For Me the intersection is when a pet trained submissive services a real animal.
As for myself I'm not big on elaborate role play or forced fantasies, but again the room is open to anyone.