In 1935 the Austrian physicist Erwin Schrodinger proposed the following thought experiment: A cat is placed in a sealed box with a device that will dispense poison if it detects the radioactive decay of a group of atoms also placed in the box. It is a given that the atoms have a 50% chance of decaying over the course of an hour. Until the box is opened we can’t know if the atoms decayed or not and therefor if the cat is alive or not.
The purpose of the experiment was to highlight the quantum principle of superposition, that is an object (in this case the atoms) in being in multiple states (decayed and not decayed) simultaneously until the presence of an observer collapses the wave form and one state becomes “true”. While the quantum particles can hold superposition, Schrodinger wanted to highlight the absurdity of a macro object like a cat being both alive and dead at the same time.
This concept has been incorporate into popular culture in ways that only obliquely references its source. Mostly, people have been using the concept in reference to people and things pocessing multiple exclusive traits, for example the Huffington Post called Mitt Romney “the Schrodinger’s Cat of corporate executives” for both being in change of and not being in change of Bain Capital.
For more information about this mind bending thought experiment, and other odd quantum phenomena, check out this article from Swapnil Srivastava: http://www.buzzle.com/articles/basics-of-quantum-mechanics-for-dummies.html