An order parameter is a quantity chosen to distinguish phases and measure their degree of order. For a conventional spontaneous symmetry breaking transition, it vanishes in the symmetric phase and acquires a nonzero value in an ordered phase once a state or symmetry-breaking limit is selected.
The magnetization of a ferromagnet is a vector example. In a nematic liquid crystal, an ordinary average molecular axis can vanish because opposite directions are equivalent, so the nematic order parameter is a tensor instead. Choosing the correct object is therefore part of identifying the order. In a finite symmetric ensemble, averaging over differently oriented ordered states can also give zero; correlations or an infinitesimal conjugate field reveal the underlying order. Some phases require nonlocal diagnostics beyond this conventional local-order-parameter description.
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