Notice that that summation in front of the is over every number from 0 to 7.Normally, you can’t ask about more than one number at a time, but because of “quantum parallelism” you can input multiple, over-lapping, numbers/states at the same time, and even interference!
(the other possibilities involve constructive interference) So, by asking a single “quantum question” you can discover instantly whether the Oracle always has the same opinion about the numbers 0-7, or has differing opinions.
Normally, you’d be stuck asking as many as 5 ordinary questions.
The photon both passes through (0) and is refelected (1).
Unlike an ordinary bit, a qbit is in both states at the same time.
Like a Turing machine, the exact construction of a quantum computer (and there are a lot of different constructions) isn’t particularly important for the philosophy behind its functioning.