The principle of painting 'fat over lean' is one of the fundamental concepts of oil painting and one to follow to reduce the risk an oil painting cracking. 'Fat over lean' has got to do with the varying drying times of oil pigments (which can vary from a couple of days to a fortnight) and ensuring that upper layers of paint don't dry faster than lower ones.
'Fat' oil paint is oil paint straight from the tube. Mixing it with an oil makes it even 'fatter' and increases the length of time it takes to dry completely (even though it may feel dry to the touch, it will still be drying under the surface). 'Lean' oil paint is oil paint mixed with more turpentine (white spirit) than oil, or oil paint mixed with a fast-drying oil. 'Lean' oil paint dries faster than 'fat' oil paint.
If 'lean' is painted over 'fat', it will dry first, making the 'lean' layer of paint vulnerable to contraction (shrinking) and cracking when the 'fat' layer dries underneath it. Lower layers also tend to absorb oil from the layers above them.Therefore every layer in an oil painting should be a little 'fatter' than the previous one or have a greater proportion of oil in it.
The drying times of artist's quality oil paints will vary because they are usually made only from pigment and oil; cheaper paints may have drying agents added to make the drying times more consistent.
Paints which tend to have a low oil content, and thus dry quickly, include Prussian blue, ultramarine, flake white, and titanium white. Oil paints with a medium oil content, and which dry within about five days, include cadmium reds and cadmium yellow.