Well, theoretically, combining qubits gives you exponentially improved computing power for starters. IBM have already built the first quantum computer (5 atoms), and were proposing a commercial application (10 atoms) this year. The main applications of qubits would be encryption, decryption, modeling, databases, voice recognition, structure recognition and artificial intelligence. There's some allegedly freaky possibilities of instantaneous information transfer, since quantum theory predicts that two "entangled" particles will share identical states - i.e. if you alter one particle's state, the other's will change instantaneously, no matter where it is in the universe (theoretically).
Regarding the theory, and how it would actually apply to a Quantum Computer - qubits are stored in registers that are represented by quantum phenomena like electron spin or photon polarization. A particle with an up spin represents a 1 and the same particle with a down spin represents a 0. Or, a photon with parallel polarization is a 1 and the same photon with perpendicular polarization is a 0. However, due to the (theoretical) nature of quantum mechanics, quantum particles don't exist exclusively in one state, rather they exist in a superposition of states. So, a qubit register can store both a 1 and 0 simultaneously—two qubits can represent 00, 01, 10, and 11—all at the same time. Hence, as I said above, as you add registers, the number of numbers you can store grows exponentially, as does the power of your computer.
I imagine that if this sort of technology is viable in the near future it would be terrific for modelling real world processes and phenomena, and would certainly be a boon to the sort of research which this site supports.
