The stone allows no light to pass through. Stones such as cabochons are naturally opaque, because they don’t let any light shine through. What they do is reflect the light. A well-cut cabochon will reflect light evenly as you slowly rotate it in your fingers, whereas a lower quality cut will make the light snake across the surface.
In grading the clarity of a gemstone, the term opaque means the stone will hardly shine at all when light is passed through it. The example of the cabochon shows how light still reflects of its surface, despite being opaque, and thus showing a better quality cut.
Naturally opaque stones do occur; however, they tend to be lower in price. Meanwhile, stones that are so flawed they are opaque rarely have any market value.