[galadran]

Note: This explanation is FAR from precise and is only trying to give an intuition

The key point is that qubits aren't limited to finite "multiple values", they can express an uncountable number of values. The best "short" answer is that a qubit can exist in a superposition (QM Term) of states. LOOSELY put it can have a probability of being a 0 and a probability of being 1 (with both probabilities adding to 1). This ability to encode information as the probability is the key to quantum computing.

When you measure (QM Term) the qubit, it takes on either the value 0 or 1 according to the probabilities you set it up with. This is computationally useful because with clever constructions you can make these probabilities meaningful.

For example Grover's Algorithm allows you to search an unsorted database for a particular item in O(sqrt(N)) time rather than the classical best O(N). The algorithm is successful with very high probability, note that because it uses the probabilistic nature of qubits, it itself can only be probabilistically correct, it just so happens you can make the probability of error very low (in theory lower than the chance your classical computer has a bit flip or similar)

The unfortunate restriction on QC is that you need enough qubits to encode your problem, if you can't hold the database in your "qubit memory" then you can't perform algorithm. In practice, building systems of qubits is extremely difficult and the current record is about 1000 as of 2015 I believe.