Bell state
A Bell state is one of four special two-qubit states that are maximally entangled — the strongest possible entanglement between a pair of two-level systems. Each is a balanced superposition of the two qubits agreeing or disagreeing, with no information at all about either qubit on its own. They are named after John Bell because they are the natural states in which to display and test the correlations his theorem concerns.
The four Bell states form a complete, mutually distinguishable set, a convenient 'alphabet' for entanglement. Any of them can be turned into any other by a simple operation on just one of the two qubits, and together they serve as the standard reference pairs in quantum information. Measuring two qubits in this Bell basis, rather than individually, is the key step in protocols like quantum teleportation and dense coding.
What makes a Bell state special is the perfection of its correlations: for matched measurements the two outcomes are guaranteed to line up (or to be exactly opposite), every single time, while each qubit measured alone gives a fair coin-flip. That combination of total local randomness and total joint predictability is exactly the feature that classical, locally-real physics cannot reproduce, which is why Bell states are the workhorse of both foundational tests and practical quantum technology.
Two of the four Bell states: each qubit alone is random, yet the pair is perfectly correlated.
Bell states are the maximally entangled two-qubit states, but entanglement is not all-or-nothing: many useful states are only partially entangled, and measures like entanglement entropy quantify where a given state falls.