A raw egg is runny.
Heat it and the same ingredients become firm.
The change happens because heat rearranges the proteins inside the egg.
Proteins begin folded into specific shapes
Proteins are long chains of amino acids.
In a raw egg, those chains are folded into particular three-dimensional shapes.
They are suspended in water.
That helps create the familiar liquid texture.
Heat causes denaturation
Add enough heat and many of the protein structures begin unfolding.
This is called denaturation.
The chains are still proteins.
They are simply no longer folded the same way.
Unfolded proteins connect with one another
Once the proteins unfold, parts that were previously tucked away can interact with neighboring proteins.
The chains begin forming a larger network.
That network traps water.
The egg changes from a runny liquid into a firm gel-like solid.
Why does cooling not turn it raw again?
The new protein network is not easily reversed.
Put a hard-boiled egg in the refrigerator and it becomes a cold hard-boiled egg.
The proteins do not neatly refold themselves into the original raw structure.
Is this the same chemistry that browns meat?
Not exactly.
Cooking meat certainly changes proteins too, but the brown crust discussed in why meat browns when cooked mainly comes from Maillard reactions between amino acids and certain sugars at the hot surface.
Egg solidification is primarily about protein denaturation and network formation.
Why do whites and yolks firm at different rates?
They contain different mixtures of proteins, fats, and water.
Those proteins respond to temperature differently.
That is why careful cooking can produce a firm white with a softer yolk.
So cooking does not simply remove enough water to make the egg solid.
Heat rearranges the proteins into an entirely new structure.
And that’s the short explanation.
Related explanations: Why does meat brown when cooked?, Why does toast turn brown?, and Why does bread rise?