P-symmetry is simply the spatial symmetry exhibited during a reflection. "P" stands for parity. Apart from orientation, reflection would mathematically mean a reversal of either one or all three axes of reference in a three-dimensional Cartesian coordinate system.
It was long taken for granted that all physical laws preserved P-symmetry, and nobody ever doubted that idea until the 1950s. Certainly all of electromagnetism and gravity (both quantum and relativistic versions) preserved such a symmetry. It would mean that, 'left' or 'right', a 'positive' or a 'negative' electric charge, 'north' or 'south' poles of a magnet, and all such things are mere naming conventions, and there is no absoluteness in the definition of a choice for such dualities. Feynman explains this assumption of symmetry by asking how we would be able to communicate to an intelligent alien as to what we mean by 'right' or 'left' (so as to shake hands with the 'right' hand, when we meet them first), without using any objects (stars, for instance) for reference, and solely through an experiment conducted by the aliens that would, in principle, show them what 'right' or 'left' is. If all physical phenomena preserve P-symmetry, then there could be no experiment we could communicate to distinguish 'left' from 'right'.
It came as a shock to most physicists in the 1950s that P-symmetry was violated in some radioactive phenomena which involved weak forces. In fact, an experiment by Chien Shiung Wu and collaborators using radio-cobalt exhibited a bias towards a spatial direction: symmetry was "not conserved under a reflection", a mirror-image experiment would have the opposite bias. Parity is maximally violated for weak interactions. This means weak interactions ONLY affect left-handed fermions. See chirality (physics). This led to a search for stronger symmetries that would be preserved. In fact, there was also evident violation of C-symmetry (charge inversion symmetry) and T-symmetry (time reversal symmetry). For some time afterwards, it was believed that a combination of the two, known as CP-symmetry, was preserved, but this was also found to be wrong. As of 2004, physicists have a theorem that maintains the preservation of a CPT-symmetry. All known laws of physics preserve the CPT-symmetry.
The well known statement, "God is weakly left-handed", refers to this P-violation.