symmetry breaking
Sit a pencil perfectly upright on its point. Every direction around it looks the same — the situation is perfectly even-handed. But the pencil cannot stay balanced; it must topple, and the instant it does, it picks one direction to fall, even though no direction was special. That sudden choice out of a tie is symmetry breaking.
Symmetry breaking happens when the laws governing a system treat all directions or options equally, yet the system in its settled, low-energy state nonetheless ends up committed to one of them. In a magnet the underlying physics does not care which way is 'up', yet when it cools the atomic compass needles all swing into one shared direction and that direction becomes real and measurable. The symmetry of the laws is broken by the actual state the material chooses, not by the laws themselves.
Symmetry breaking matters because it is the deep reason ordered phases exist at all: crystals, magnets, even the Higgs mechanism that gives particles mass are all stories of broken symmetry. A frequent confusion is to think the symmetry is 'destroyed'. It is not — the full set of possibilities is still equally allowed; the system has simply landed on one of them, and which one is a matter of chance or the tiniest initial nudge.
When water freezes into a snowflake, the liquid had no preferred direction — it looked the same whichever way you turned it. The ice crystal that forms suddenly does have special directions, locked into its six-fold pattern. The roundness of the liquid is traded for the picked-out axes of the crystal: symmetry broken.
Freezing breaks the 'all directions equal' symmetry of a liquid, choosing the fixed axes of a crystal.
There is a quieter point here: even though each material picks one outcome, a huge collection of them would, on average, pick all outcomes equally. The symmetry survives in the statistics; it is only broken for each individual realized state.