This blend mode does comparatively more complex task. If you paint an area with a color that is darker than neutral gray, the resultant area will be darker. But if you paint an area that is lighter than neutral gray, the resultant area will not show any effect. In short, it only darkens the image.
Refer Fig. 6.6 for more clarification. I have painted the baby’s cloth with a color that is darker than neutral gray color. So the resultant color is a darker shade of gray. In Adobe’s words: Looks at the color information in each channel and multiplies the base color by the blend color. The result color is always a darker color. Multiplying any color with black produces black. Multiplying any color with white leaves the color unchanged. When you’re painting with a color other than black or white, successive strokes with a painting tool produce progressively darker colors. The effect is similar to drawing on the image with multiple marking pens.
5: Color Burn
Works same as Multiply blend mode, the only thing different here is that it results in greater contrast.
In Adobe’s words: Looks at the color information in each channel and darkens the base color to reflect the blend color by increasing the contrast between the two. Blending with white produces no change.
6: Linear Burn
Works same as Multiply blend mode, the only difference here is that it dims the brightness.