In an ordinary computer, a transistor can be either on or off, so a bit is always either 1 or 0. An alternative is to exploit quantum physics, and to store information using single quantum particles such as electrons. One might store bits in an electron's spin, for example, which can be either "up" or "down". The key is that the quantum world also allows other seemingly nonsensical possibilities: an electron's spin can be neither up nor down, but in a superposition of both. So a string of electrons can hold not just one distinct string of 0s and 1s, but every conceivable string all at once.
As a consequence, a computer handling information in quantum fashion could do parallel processing on an outrageous scale, testing many possibilities at the same time. In 1997 mathematician Lov Grover of the IBM Research Division showed that a quantum computer can search a database far faster than any classical device. It starts with a superposition of all the different items in a database, and alters this quantum state to amplify the desired item and make the others fade away. For a huge database, the time savings are huge, and even for smaller values of N the quantum procedure is faster.
Buchanan, M. 2000, 'Life force', New Scientist, 15 April 2000.