There are different interpretations of quantum mechanics and all of them are more philosophy that actual physics. This is because all of them make the same predictions. The real problem is not with quantum mechanics, it is with making a human understand quantum mechanics.

One of these is the many worlds interpretation. In this way of thinking, the Universe forks to realise everything that could happen from the given initial conditions. When you make a measurement you just try to figure out in which of the possible Universes you happen to live.

In quantum computing you carefully set up a quantum system that is able to do a simple computation. In the many worlds interpretation, the system will now do all possible computations at once (but creating different forked Universes), and whenever you measure you will find which one it did in the Universe you live in. So it did do only one operation, just like a classical computer.

So where is the advantage. In a classical system you will always find the same answer if you repeat the same operation. For a classical computer to find a different answer, takes as much time as to set up the system for a different computation. In a quantum computing system this is no longer needed. You only need to wait a very short quantum time-scale and repeat the same operation. This time your path through the web of all possibilities is different and you find another answer to a different question. In practice this timescale is so short that when you measure, you directly obtain a superposition of all possible computations (doable in the system you prepared) at once.