Parity is both an operation and an intrinsic property used to describe particles and their wavefunctions (mathematical representations of one or more particles) in quantum mechanics (a branch of physics focusing on particles smaller than an atomic nucleus).
The parity operation is a combination of a left-right trade (mirror reflection) with a top-bottom switch. This combination is also called a spatial inversion. How objects behave under a parity operation defines their intrinsic parity. All microscopic particles have an intrinsic parity that helps us tell them apart. An object or group of objects that is the same before and after a parity operation is called parity invariant. A parity invariant object has "even" or "+1" intrinsic parity. If the parity of an object changes due to a parity operation, it has "odd" or "-1" intrinsic parity.
Even though people do not obey reflection symmetry (their right and left sides are different), scientists believed that the laws of physics were parity invariant. In 1956 a Chinese-American scientist named Tsung Dao Lee figured out that the idea of parity invariance had not been tested in relation to one of the fundamental forces of physics, the weak force (responsible for spontaneous decays of some microscopic particles). This prompted Lee and a colleague, Chen Ning Yang, to think of a clever experiment to test the parity invariance of the weak force. Later in 1956 Dr. Chien-Shiung Wu carried out this difficult experiment using a radioactive (spontaneously decaying) element called Cobalt. Wu observed the direction of electrons (smallest naturally-occurring charged particles) coming out of the Cobalt due to its radioactive decay. She found that the electrons did not come out the way she expected. Thus this experiment was not parity invariant. Since it tested the weak force, this meant the weak force was not parity invariant either. This result was so important that Yang and Lee won the 1957 Nobel Prize in physics for it. Now we know when we see parity invariance the weak force is the culprit. All other fundamental forces are parity invariant.
Parity is often studied along with charge conjugation. Charge conjugation changes a particle into its opposite, or antiparticle, by changing the sign of its electric charge. Even though parity is not conserved by itself, it was thought that the combination of parity (P) and charge conjugation was conserved. In 1964, however, physicists J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay discovered that CP conservation is not obeyed by studying the decays of particles called Kaons. Scientists know that the laws of nature must obey conservation of the combination of parity, charge conjugation, and time symmetry (T), because of the way they are formulated. This is called CPT symmetry. Because CP symmetry is not conserved, it follows that time symmetry must not hold, so that total combination, CPT, can be conserved.