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I think the book means that that resonance is the hybrid of all the resonance structures, or all the structures together. This is the actual structure of the molecule. 1.5 bond is the average of a single bond and a double bond.
Resonance structures occur when there are multiple places where you could put a double/triple bond and all the possible variants would still be equal. The real structure would be a combination of all the resonance structures, therefore making a fractional bond length that is the average. The only reason we draw all the resonance structures is because it would be too hard to indicate the real structure through freehand drawing alone.
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