A hen’s egg contains a small air pocket just inside the shell at the broad end, the purpose of which is to let the chick breathe while pecking its way out on its birthday.
Because the shells are porous and permeable to gases, outside air can diffuse in and exchange with the air inside. As an egg ages and its contents shrink away from the shell, more air comes in to fill the space and the air pocket grows larger.
A really fresh egg will sink in water, but as it ages and the air pocket grows bigger, it will tend to turn its broad end up. Eventually, a stale egg will float entirely on the surface.
When you cook an egg, heat expands the air in the pocket and its pressure increases. As long as the white is still liquid, it can’t flow into that air space because of the pressure. As the white cooks, it solidifies around the shape of the air pocket. Hence the dimple.
And by the way, those ropes of thick albumen that extend from the yolk to the membranes at both ends of the egg and that hang on to the yolk when you’re separating an egg are not the beginnings of an embryo.
They’re called chalazae (kuhLAYZ eye), a word inexplicably derived from the Greek meaning “hail.” They serve to keep the yolk centered in the white.
Chalazae are more prominent in very fresh eggs. There’s no need to remove them, except perhaps if you are making a soufflé or a custard and want it to be as lump-free as possible.