entanglement
Entanglement is a shared quantum state in which two or more particles can no longer be described separately, even when they are far apart. Once entangled, the pair has a single, joint wavefunction; asking about one particle alone is like asking for the first half of a rhyme without the second. Their properties are correlated in a way that has no honest description as 'this particle has these traits, and that one has those'.
The classic image is a pair of particles prepared so that their spins must point in opposite directions, yet with neither direction fixed in advance. Measure one and you instantly know what the other will give for the matching measurement, however many light-years separate them. The correlation is real and reliable, but it is not a hidden message passed between them; nothing about the result you get on your side can be steered or used to send a signal.
Entanglement is not a faint, exotic effect but the generic situation for interacting quantum systems — the rule rather than the exception once particles have met. It is the resource behind quantum computing, quantum cryptography, and teleportation protocols, and it sits at the heart of the deepest puzzles about how the quantum world hangs together. What it overturns is the comfortable assumption that the whole is always just the sum of independently-real parts.
A joint state that no product of two single-particle states can reproduce — the signature of entanglement.
Entanglement gives perfectly correlated outcomes, but it cannot transmit information faster than light. Each side, looked at alone, sees only ordinary random results; the correlation appears only when the two records are later compared.