Madame Wu discovered the parity violation in beta-decays. To do so, she took some Co-60 nuclei, which decay via beta-decay in Ni-60 with emission of electron, antineutrino and 2 gamma rays. She aligned the magnetic momentum of the cobalt nuclei with a strong magnetic field and then... I can't really see what she would have expected to see and what she found instead. I hope someone could explain this to me.
The big mystery is: why should nature prefer one direction over another? And the answer is still unknown.
From wikipedia: The experiment's purpose was to establish whether or not conservation of parity (P-conservation), which was previously established in the electromagnetic and strong interactions, also applied to weak interactions. If P-conservation were true, a mirrored version of the world (where left is right and right is left) would behave as the mirror image of the current world. If P-conservation were violated, then it would be possible to distinguish between a mirrored variation of the world and the mirror image of the current world.
The experiment established that conservation of parity was violated (P-violation) by the weak interaction. This result was not expected by the physics community, which had regarded parity as a conserved quantity.
As opposed to the symmetry expected, in fact 60 % of the gamma rays were emitted in one direction and 40 % in the other. In beta decay, if parity conservation was observed, the electrons should have no particular direction of decay, relative to the nuclear spin of the cobalt atoms. In fact they were (mostly) emitted in a direction opposite that of the nuclear spin.
Have a read of the full wiki article with links to concepts behind it, experimental details and the ramifications of her results on the standard model, including time reversal.
BTW, thanks for asking this question, I needed to study it myself this week!