I'm familiar with using white / silver / gold reflectors to add fill light to a photo. When would you use a black "reflector"?
To remove light.
If you're shooting outside, or in a place where there's lots of background light being bounced around, it might not be enough to place an item to create a shadow onto your object, since light reflected off of that item might still give you tints or light you don't want.
A black "reflector" creates shadow and doesn't reflect light (or as much light, depending on the quality) onto your object, which might help you darken it.
For instance, if you're trying to take a portrait outside, and the face gets a bit too much light on one side, a black reflector might help you reduce that by both creating a "shadow" by blocking light, and not reflecting any light onto that side of the face.
Basically, it's to subtract light. It can reduce bounced light or provide isolation of your subject to make it stand out more. I do this all the time with things like smoke photography because it eliminates stray light and provides a clean, dark, background for the smoke to stand out. For example:
Imagine your subject in a very small room, and the walls are painted in red.
A large window is giving you some very lovely soft light on the subject's face. You have decided there is no need for fill light (either because the light is soft enough, or you are happy with the contrast/shadow).
But wait, since the room is so small, the sunshine is hitting on the red wall, and it is bouncing an awfully red tint on your subject's face.
You want the interior of the room as background, but the strong red tint in the model's face is just awful.
Well, using a black reflector, positioned closely to the shadow side of your subject's face, you will remove the red cast without adding fill light, so you can keep the mood you want with natural light.
Sometimes when taking photos of shinny objects, you want to be able to block reflections of unwanted lights. Say you are shooting a stainless steel watch next to a Christmas tree (just a crazy example, I doubt if anyone would do that in a real world setting), you may not want the reflections the rainbow of lights of the Christmas tree on the watch. You can use a black reflector to cut it out.
Having a black surrounding also makes the sparkles that you do want to keep stands out more.
Black is a "dark reflector". Think of it as of "anti fill light". It really works that way, just like the white reflector, but subtly adding shadow instead of fill light. It takes time to learn how to use it, as the concept of "dark light" is unnatural and non-intuitive, but after all it's just a tool like all others.
A black reflector has several usages. The main one is to block light when you have a light environment and you want darker shadows on that side.
On this example, the "studio" has white walls, and you want a more dramatic shadow, so you need to "absorb" some of the lights on the shadow side, so it does not bounce back.
It is very important when taking photos of glossy objects, for example, jewelry. You are not only taking the photo of the object but also of the surroundings because they show on the reflective surfaces.
And I would say that they are indispensable for transparent objects. Remember that the size does not matter, they can be small, you want to control where you are blocking the light.
When you use them to block incident light they are also called flags. A flag does not need to be black, it is simply projecting a shadow.
Of course, they are normally out of the frame. I left them inside so you can see them.
And in some cases, you can use them simply as backgrounds.