In Quantum Mechanics the physical systems are described by wave functions or density operators. When the same wave function describes two or more subsystems, like two photons for instance, their properties can be highly correlated. This correlation can be so high that they are said to be nonseparable or entangled. This means that their global properties are well defined, while their individual properties are completely undefined. In this case, the measurement of the properties of a subsystem provides information about the other subsystems that were not measured. The so called EPR (Einstein-Podolsky-Rosen) paradox can be explained in terms of two photons entangled in their polarizations. Two entangled photons are produced and each one are sent to a different detection station. They are entangled in their polarizations. If one tries to determine the polarization of each photon individually, one finds that it is unpolarized. However, if one measures one photon in some polarization state, say linear horizontal, the other photon will be in a well defined state, say also linear horizontal. One distinction from a classical correlation is that the quantum correlation can be observed no matter what measurement basis one choses, that is to say, linear, circular polarization or other.
The discussion about entanglement and stronger than classical or quantum correlations started right after the construction of the Quantum Theory in the beginning of the last century, motivated by the EPR paper published in 1935. In 1965, John Bell found a way to experimentally test if these correlations could be described by a classical theory known as hidden variables theory. Since then, several experiments have demonstrated that these correlations are really quantum and cannot be explained by a hidden variables model. More recently, in the eighties, it was found that quantum entanglement can be used as a resource for speeding up computations and increasing security in communication channels. These new ideas started what is now known as Quantum Information Science, a branch of the knowledge that tries to use special properties of quantum systems to improve computation and communication tasks. An even more recent line of research called Quantum Thermodynamics tries to interpret quantities from the Thermodynamic theory, like work and heat, in the context of the quantum world.