A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model. Unstable domain walls can also appear if spontaneously broken discrete symmetry is approximate and there is the metastable vacuum.
A domain (hyper volume) is extended in three spatial dimensions and one time dimension. A domain wall is the boundary between two neighboring domains. Thus a domain wall is extended in two spatial dimensions and one time dimension.
Important examples are:
Domain wall (magnetism), an interface separating magnetic domains
Domain wall (optics), for domain walls in optics
Domain wall (string theory), a theoretical 2-dimensional singularity
Besides these important cases similar solitons appear in wide spectrum of the models. Here are other examples:
Spontaneous breaking of discrete symmetries at early cosmological epochs can produce domain wall. Formation of domain wall network influence on the late stages of cosmological inflation and the cosmic microwave background radiation. Observations impose severe constraints on the existence of stable domain walls. Those constraints should be accounted for by the models of the beyond Standard Model physics. Unstable cosmic domain walls decay also should produce potentially observable radiation.