If the egg does not get fertilized, the yolk then journeys on to the magnum, where the albumen (what we commonly call the egg white) is formed around the yolk.
Over the course of a 24-hour stay here, the shell is created around the soft innards of the egg in a process that sees layer after layer of white shell effectively "painted" on by the gland pouch.
Once the shell is formed, a white egg-laying hen will experience uterine contractions and eventually lay the egg.
Creating this brown pigment daily takes more energy and nutrients, and therefore more food. Hens that lay brown eggs have to eat more feed than hens who lay white eggs.