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Symmetry breaking, the loss of some symmetrical aspect of something, is considered part of physical processes, such as some phase transitions. Spontaneous symmetry breaking is a break in some kind of symmetry that "happens by itself", typically really tied to a change in energy density or temperature. Typical is that at a higher density or temperature, some structure is in a stable, symmetrical state, but if they fall, there is a point in which the stability is lost, and slight perturbations (which might be inevitable) allow it to settle in a state without the symmetry.
An "everyday" situation with an analogous break in symmetry is that of either a ball within a symmetric rounded valley or on a symmetric rounded hill. In the former case, the ball's position is stable, and the whole setup is symmetric, but in the latter, a slight disturbance will send the ball down the hill, and the whole setup has lost its symmetry. The force fields of physics have features equivalent to such hills and valleys.
In cosmology, it is assumed that at one time, there was just one force rather than the four (defined by the Theory of Everything (TOE)), and that with the breaking of symmetries as temperature/energy-density fell, this divided into gravity versus a combination of the three (Grand Unified Theory, GUT), and later divided into the strong force and electroweak, the latter of which broke into the weak force and electromagnetism.