Why was there a sharp increase in the margin of support of independence in Scotland in August/September 2014?
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Any answer to this question will inevitably be somewhat speculative. However I think there were two main factors:
The approaching referendum, meaning that previously undecided people started picking a side. Many seem to have come down on the "Yes" side.
The second Salmond/Darling debate, which Salmond was widely viewed as having won.
It also seems likely, given that the final referendum result was 45-55 whereas the preceding opinion polls were more like 47-53 if you ignore the undecideds, that there was a degree of polling error.