Ok, the story of the egg...

The white is what becomes the chicken. That's why it's pretty much solid protein. Everything in the white is the basic cellular structure of a chicken. Beaks, feet, feathers, bones, organs, all that.

The yolk is the 'food sack' which the chick embryo feeds off of through it's development. Which is why it's the fat content of a whole egg. Any animal that has a live birth feeds the embryo/fetus through the mother's body (via the umbilical cord). Anything hatching from an egg needs it's own self contained nutrient source in order to grow before the 'birth' happens. That's what the yolk is.

The little white 'string' that you see when you're separating eggs, the part that will never seem to mix when you're scrambling eggs, is essentially the umbilical cord. It's what connects the developing embryo to it's nutrient source (the yolk) in the same way that a fetal human is connected to it's mother's nutrient supply. The exception being that the connective tissue will break away on it's own when the nutrient reserves of the yolk is exhausted and the chick is ready to hatch.