Why does egg white stiffen when whisked?

Egg white is 90% water. It also contains long protein molecules which keep a propagation of the water molecules loosely connected. In their normal state, the proteins are in the form of dense spheres which can best be compared to balls of wool. When egg white is whisked until stiffens, two things happen: air bubbles form in the water and protein mixture and the protein molecules unravel. Because they consist of both hydrophilic (water-loving) and hydrophobic (water-repelling) parts, they attach themselves to the boundaries between the water and the air bubbles and so encapsulate the air bubbles - with the result that the egg white becomes stiff.

if the egg white is beaten too much, however, the water can detach itself from the proteins again and the process will fail.

Traces of egg yolk can also cause problems. This is because its molecules weaken the coating around the air bubbles and make it harder for proteins to attach themselves. Egg yolk and other fats only cease to be a problem once the egg whites are stiff.