A quiet conversation in the darks is simply the marks or shapes that are black or almost black, within the larger, dark areas of your art. For example, if your picture is a white bird with a dark green jungle background, then the tree branches and the leaves, provided they are almost as dark as the surrounding jungle, would be the quiet conversation in the darks. Those leaves and the tree branches are very subtle as they are dark in value, sitting on top of that jungle background that is also dark in value.
On the right side of the diagram above, the smaller triangle, star and circle are the quiet conversation because they are close in value to the black shapes they appear upon. The close value relationships of the quiet conversation can provide subtlety and sophistication to your art.