A quantum computer is a computer that uses quantum information to store data. In a classical computer, data is stored electrically, via a 0 (off) or a 1 (on). Quantum bits (called Qubits) can exist in a superposition of possible states simultaneously. They are, in other words, non-binary.
Dwave's older, 128-wire chip
D-Wave's systems are not this sort of quantum computer. D-Wave's computers use a type of computation known as quantum annealing, in which the interacting bits being used to solve an equation are dropped into their lowest energy state. This process -- if done extremely slowly -- creates a solution to the problem in question. One of the caveats of D-Wave's systems is that the chips work best when problems can be mapped directly on to the super-cooled circuitry.
D-Wave's chips, in other words, aren't general purpose computing devices. These aren't products that'll ever replace the Intel or AMD processor in your current box; they rely on cooling the CPU down to temperatures best measured in Kelvin, not Celsius. But when you hand them problems they can solve, they're extremely quick. The system NASA and Google are buying can eventually be upgraded to a 2048-bit chip (from the current 512-bit version) when it becomes available.
Researchers have been slow to hail D-Wave's computer as a genuine quantum computer, partly because the company has been tight-lipped about the capabilities and function of its processor, but several published papers have increased confidence. The general consensus is that D-Wave's systems are performing some quantum operations, even if they don't represent a full quantum computer as classically conceived. One of the differences between the D-Wave quantum system and a conventional CPU is that flaws in the D-Wave processor that limit the number of bits it can compute with at a given time don't fundamentally compromise the chip's function. Improving yields, however, remains a focus of the company's efforts.
In the right circumstances, D-Wave's solution can be up to 10,000 times faster than current conventional silicon. As we've said, that speed boost isn't a guarantee -- code has to map fairly precisely to the chip's capabilities to make that happen -- but it's a huge increase at a time when conventional silicon scaling has faltered. D-Wave's systems aren't likely to lead to a fundamentally new means of building consumer products, but driving huge increases through enterprise and scientific computing could help us find the replacement for silicon that the entire semiconductor industry is currently hunting for.