I tried to find out on line a succinct explanation what mediates foetal stem cell ( presumably in a blastocyst ) differentiation into specific organs ( presumably following gastrulation ) during development but just got totally confused . Can some kind person tell me ?

Their environment. The cells respond to gradients in differentiation factors, as well as to the cells that are around them.

Bluenoise's answer is generally correct, but the situation is much more complicted for ES cells. Concentration gradients apply later in development. They have been well-studied in limb development and patterning. The concentration of 2 or more factors, for instance, tells an undifferentiated cell (but no longer an ES cell) to become a bone cell at a particular place in the limb.

 

ES cells make their own differentiation factors and these act on the cell and on neighboring ES cells. It's called "autocrine/paracrine" action. ES cells must be stopped from differentiating. In cell culture this is done by either culturing the ES cells on a layer of killed mouse 3T3 cells or including Leukemia Inhibitory Factor (LIF) in the culture media. When LIF is withdrawn, the ES cells differentiate in random patterns. You will have a heart cell next to a bone cell next to an intestinal cell next to a nerve cell.

 

When ES cells are implanted in a mass into an animal, basically the same random differentiation pattern happens. The result is a teratoma where you will have mixture of teeth, hair, intestine, muscle, cartilage, bone, etc.

 

Scientists are just now figuring out what the differentiation factors are. And this is one area where ES cells are critical. No other cell is going to be able to be used as an assay for these very early developmental differentiation factors.