Quantun Entanglement was first predicted by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935.
It has now been (unequivocally) experimentally demonstrated with photons, neutrinos, electrons, and even molecules such as buckyballs and small diamonds.
It's defined as :
[…] a physical phenomenon that occurs when a pair or group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others, including when the particles are separated by a large distance. Source: Wikipedia
Since the entangled particles can be separated by any distance, a problem arises as to whether the effect is 'instantaneous' - if it is, then 'information' travels faster than lightspeed, which is strictly prohibited in the current Standard Model of physics. If the transfer isn't 'instantaneous' then current explanations of entanglement are lacking detail.