basically it is this. the quantum computer is given a problem to solve, the way it solves the problem is by looking at all of the possible solutions at once ( an infinite number ) and the correct solution *pops* out.
here is an example, say the constant of the universe was 5 and the equation to solve it would take a bzillion years for a normal computer to calculate it. well a quantum computer looks at it like this
_____5
...1234 678...
it looks at the equation and the answers from negative infinity and positive infinity and the correct answer pops up, and it can easily say, "hey, that one is the correct answer because it is popping up".
as far as the details about how it exactly works i do not fully know, but that is the general idea.
EDIT: adjusted the 5 so it was above the gap