Essentially, they modify whether the blend color is applied to the foreground or background layer. When the behind mode is selected for example, a color will be applied behind the layer showing through only int he blank or transparent areas. The Multiply mode multiplies the brightness of the base color and the blend to create a darker tone. The opposite effect can be achieved by using Screen Overlay works like screen and multiply depending on the value of the base color. Specifically, the hues of the base color will move towards the blend color.
Soft light works like overlay with less intensity while Hard light is more intense.
Darken darkens the base color using the blend color as a basis and Lighten lightens the base color by using the lightest value of the blend color. Difference compares the brightness values of the base and blend colors and creates a result value by subtracting the smaller from larger values. Hue replaces the hue of the base with the hue of the blend. Saturation does the same for saturation and Color does the same for both hue and saturation. Luminosity works the same way for the lightness value.