When one looks at a physical problem that involves measuring a displacement, one has to make a decision over what direction to define as positive. Suppose we are looking at a box on a table that can be pulled by a rope. One person might define motion to the right as being in the positive direction, and so would say "the box is accelerating to the right, which is positive, and so the force must be in the positive direction." However, another person could say motion to the left is positive, so they would say "the box is accelerating to the right, which is negative, and so the force must be in the negative direction." The point is that both people agree that the acceleration and the force are in the same direction, in accordance with Newton's second law. Deciding which direction to call positive is a human choice and shouldn't affect the physics.
The idea that the choice of direction does not matter is referred to as conservation of parity. What this means is that if we go through all the equations describing nature and replace (+x,+y,+z) with (-x,-y,-z), they should still make as much sense. Physicists say that the equations are symmetric under parity exchange. These ideas are often explained in terms of reflection in a mirror. The basic idea is that a process should look just as sensible when viewed in a mirror. (This is not completely accurate, however, as a mirror reflection reverses only one direction, whereas a parity inversion reverses all three.) What we choose to call a positive direction is up to us - surely nature does not mind which way round things are.
It therefore came as a great shock to physicists when they found in 1957 that nature does have a preferred sense of direction. This was discovered by Chien-Shiung Wu and co-workers, who were looking at the -decay of cobalt-60 nuclei. A sample of cobalt-60 was cooled to just above absolute zero, and a magnetic field was applied. Now, all fundamental particles possess a property called spin. It is a purely quantum mechanical phenomenon, but for this discussion we can think of it as being like the spin that a top has. The arrangement of the fundamental particles (up and down quarks in this case) in the cobalt nucleus means that it too possesses spin. Cooling the cobalt and applying a magnetic field causes the nuclei's spins to 'line up' - that is, they all spin in the same direction.
The parity rules implied that the electron from the -decay should be emitted equally in all directions. However, this was not the case, as shown in the figure:
Another example of parity violation is the spin of the neutrino. Neutrinos have their spin axis in the same direction in which they are moving. There are two possible ways in which they can spin, as shown in the figure:
According to the parity rules, both types of neutrino should exist. In fact, only left-handed neutrinos are ever observed in nature.
Whether they liked it or not, physicists had to accept that not all the laws of nature are symmetric under parity exchange.