Blending modes are a little difficult to explain. Basically, when one layer is above the other, the computer uses a bit of programming to decide how the combination of both layers will look.
Blending modes can not just apply to Layers, but also to individual strokes.
Let's start explaining with the Normal Blending mode: As you may have guessed this is the default Blending mode for all layers.
In this mode, the computer checks on the upper layer how transparent a pixel is, which colour it is, and then mixes the colour of the upper layer with the lower layer measured by transparency.
These blending modes are based on simple maths.
Adds the numerical values of two colours together:
Divides the numerical value from the lower color by the upper color.
This, unlike regular substract, will consider 0,0,0 the lowest number.
So black(0,0,0)-grey(0.5,0.5,0.5) doesn't become grey, but stays black.
Multiplies the two colors with each other, but does not go beyond the upper limit.
This is often used to color in a black and white lineart. One puts the black and white lineart on top, and sets the layer to 'Multiply', and then draw in color on a layer beneath. Multiply will all the colour to go through.
White(1,1,1)xWhite(1,1,1)=White(1,1,1) White(1,1,1)xGrey(0.5,0.5,0.5)=Grey(0.5,0.5,0.5) Grey(0.5,0.5,0.5)xGrey(0.5,0.5,0.5)=Dark grey(0.25,0.25,0.25)
White(1,1,1)-White(1,1,1)=Black(0,0,0) White(1,1,1)-Grey(0.5,0.5,0.5)=Grey(0.5,0.5,0.5) Grey(0.5,0.5,0.5)-Grey(0.5,0.5,0.5)=Black(0,0,0)
HSI is a color coordinate system, using Hue, Saturation and Intensity to catagorise a color. Hue is roughly the wavelength, whether the colour is red, yellow, green, cyan, blue or purple. It is measure in 360°, with 0 being red. Saturation is the measurement of how close a color is to grey. Intensity, in this case is the tone of the color. What makes intensity special is that it recognises Yellow(rgb:1,1,0) having a higher combined rgb value than blue(rgb:0,0,1). This is a non-linear tone dimension, which means it's gamma-corrected.
This takes the Intensity of the colours on the lower layer, and combines them with the Saturation and Hue of the upper pixels.