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Quantum computers promise to perform calculations believed to be impossible for ordinary computers. Some of those calculations are of great real-world importance. For example, certain widely used encryption methods could be cracked given a computer capable of breaking a large number into its component factors within a reasonable length of time. Virtually all encryption methods used for highly sensitive data are vulnerable to one quantum algorithm or another.
The extra power of a quantum computer comes about because it operates on information represented as qubits, or quantum bits, instead of bits. An ordinary classical bit can be either a 0 or a 1, and standard microchip architectures enforce that dichotomy rigorously. A qubit, in contrast, can be in a so-called superposition state, which entails proportions of 0 and 1 coexisting together. One can think of the possible qubit states as points on a sphere. The north pole is a classical 1, the south pole a 0, and all the points in between are all the possible superpositions of 0 and 1 [see "Rules for a Complex Quantum World," by Michael A. Nielsen; Scientific American, November 2002]. The freedom that qubits have to roam across the entire sphere helps to give quantum computers their unique capabilities.