Quantum computing is sortof like... destructively interfering all the non-solutions so the only likely measurement results are solutions.

The state of the computer is a vector of complex amplitudes (one entry per possible answer, n qubits -> 2^n possible answers). The operations of the computer correspond to unitary matrix multiplications against the state vector. An entry's probability of being the result is the squared length of its final amplitude.

I try to explain it better here: http://twistedoakstudios.com/blog/Post2644_grovers-quantum-s...