Quantum mechanics tells us that the qubit (coin) can exist in any linear superposition of heads and tails. To express this you write a|heads> + b|tails> the only constraint is that a^2 + b^2 must equal 1. Now why would that be the constraint? It is because a^2 and b^2 are the probabilities of measuring heads and tails respectively.
In this example the coin is put into the state where an and b equal 1/sqrt(2) to give an equal probability of each outcome. So there is exactly one state associated with the coin. Now this state does lead to two possible outcomes but the underlying state (that can not be directly observed) is exactly one thing.
In this example the coin is put into the state where an and b equal 1/sqrt(2) to give an equal probability of each outcome. So there is exactly one state associated with the coin. Now this state does lead to two possible outcomes but the underlying state (that can not be directly observed) is exactly one thing.