This is fascinating!

Finally my degree (Molecular Genetics) can be useful!It’s all about protein gradients. It’s part of why life is mostly symmetrical or radial. You have a point of origin, let’s say a shoulder area, producing a particular protein during development. As the cells near it replicate to form an arm, the protein made at the origin spreads into them. The further the cells are from the origin, the less protein they have. Eventually, the cells are far enough away that the lack of that protein signals that the new cells being formed should be hand cells. Those hand cells then function as a new point of origin for a different protein radiating outward, which when present on its own forms finger cells and when mixed with the original shoulder protein forms wrist cells. At about a 50/50 mix of hand/shoulder proteins, elbow cells form.This is a very simplified explanation, as the truth involves the interaction of countless protein gradients and combinations from tons of origin points, but it’s the general way that your body forms and differentiates.So the cells on the tip of your nose are far enough from the point where your nose meets your face and have little enough of one or, more likely, five thousand nose proteins that they know they should be tip of nose cells as opposed to anything else. They’re obviously not getting “please become feet” proteins because the origin cells for those are much too far away.Hope that helps.

Source:

More great discussion here:
How does the cell on the tip of my nose know to perform all the functions of a cell on the tip of my nose? How does it know that it isn’t a cell on the side of my nose (or my liver, brain, etc.) : askscience