Earlier quoted context omitted.
It's accurate. QC is just linear algebra with complex numbers, plus probability extended to the complex domain. Why that's useful is something I'm still struggling with as well.
I'd assume it's the speed advantage, but the only problem I can think of that would require that type of exponential speed is cracking hashing algorithms which just seems destructive and counterproductive, like building a digital nuclear bomb - and from my very limited understanding that's a long ways off from being achieved. I assume there's probably many more complex computational problems outside of my domain that…
More precisely, given f: 2^n -> {0,1} which is guaranteed to hit 1 exactly once, Grover finds the one input which hits 1, and it does so using about 2^{n/2} queries of f; but the constants happen to line up so that when n=2, exactly one query is required.