A quiet conversation in the lights is simply the marks or shapes that are white or almost white, within the larger light areas of your art. For example, if your picture has an almost white bird with a dark green jungle background, then the white feathers on that bird would be the quiet conversation in the lights. Those feathers are light in value and very close in value to the body of the bird.
On the right side of the diagram above, the smaller triangle, star and circle make up the quiet conversation because they are close in value to the white background. The close value relationships of the quiet conversation can provide subtlety and sophistication to your art.