Is this black substance on our wall dangerous?

That sounds like a mold growing there. Try a little bleach water or if your afraid the bleach will ruin the finnish of the wall,there are fungicides/mildewsides available at the hardware store. If this area is moist all the time or perhaps only when the shower is used, then you have a leak you'll have to track down and repair. otherwise, you'll never get rid of the mold.