They are faster because the type of operations that they can perform puts them in other complexity classes.

In particular, it is possible for a quantum computer to use entanglement for storing the "same variable" at multiple locations at once. Measurement can also be used for driving computation, by limiting the possible state-space of variables that are entangled to the one that you observe. That way you gain access to methods of computation that are not available for classical machines.

See "EPR-pairs" and "measurement" for more details. (Use wikipedia, for example.)