A term used by oil painters to describe their process.
They begin with thin non-oily paint. i.e. the lean stuff, and then they increase the thickness/paste and oil content as the painting progresses towards completion.
This is an important and constructive work-around to a problem. Oil paintings are usually built up in a series of layers. The thicker impasto layers take longer to dry, and shrinks slightly in the process.
If you worked in the opposite order. i.e. from fat to lean, then lean paint is laid over thick, and that would cause the top layer to dry first and then it would crack because the lower thicker layers shrink.