Fat over lean refers to a 'rule' in oil painting where each layer of paint should be fatter (have more oil) than the earlier layer. This is to avoid the paint cracking as it dries.
The reasoning behind this rule is based on the different drying times of oil paints and mediums. The fatter the oil paint, the slower it dries. If a layer of paint at the top dries before a layer below it, the paint will crack as it dries.
You can make oil paint fatter by adding more oil medium and you can make it leaner by adding a solvent or paint thinner. Oil painting, especially wet on wet, becomes a delicate balance of thinner and oil medium.
In practice, oil painters start with a very thin layer of paint mixed with solvent. This is almost just a faint wash of color. For each subsequent layer of paint, more oil and less thinner is added.