What does it mean by having a quantum fidelity of 0.85?

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What does it mean by having a quantum fidelity of 0.85?
 
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The fidelity can be viewed as a meassurement of distance between quantum states. If the fidelity is close to one, the states are close.
 
DavidK said:
The fidelity can be viewed as a meassurement of distance between quantum states. If the fidelity is close to one, the states are close.

I still don't understand. What do you mean by close? Do you mean like how near one wavefunction say, A to resemble another wavefunction, say B?
I stumbled on this paper on the arXiv: http://www.arxiv.org/abs/quant-ph/0406205
that's how I got to know this term.
 
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