"Fat over lean is better understood if considered as 'flexible over less flexible'. When painting in layers, the proportion of medium used in each layer should be increased. The higher proportion of medium makes subsequent layers more flexible and prevents the painting from cracking. This rule has traditionally been kept by adding more and more oil to the solvent used..."Cracking is caused by the different drying times of the oil pigments. Basically, the upper layers of paint will crack if they dry and become less flexible than the paint beneath it. In order to paint "fat over lean" you have to ensure that the upper layers of paint don't dry faster than the lower ones do.
"Fat" oil paint is paint that has an abundance of oil in it. Paint out of the tube is considered "fat", but mixing it with an oil (or medium) makes it even "fatter". The fatter the paint mixture the longer the paint takes to dry. "Lean" paint is made by mixing paint with a thinner (like turpentine or mineral spirit). As mentioned, "leaner" oil paint dries faster than "fat" oil paint because oil slows the oxidation process (or drying).
To complicate matters, the lower layers of oil paint tend to adsorb oil from the layers of paint above them. For this reason every layer of paint should have more oil in it than the previous one had. Some colors also have a lower oil content than others do right out of the tube (this is why some colors dry faster than others). Paints with less oil include all umbers, Prussian blue, ultramarine, and flake white. Oil paints made with more oil include cadmium reds and cadmium yellow. Lastly, some mediums include drying agents that speed-up the drying time. This also affects the "fat over lean" calculations an artist must make.

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