Nested cross-validation is used to avoid optimistically biased estimates of performance that result from using the same cross-validation to set the values of the hyper-parameters of the model (e.g. the regularisation parameter, $C$, and kernel parameters of an SVM) and performance estimation.  I wrote a paper on this topic after being rather alarmed by the magnitude of the bias introduced by a seemingly benign short cut often used in the evaluation of kernel machines.  I investigated this topic in order to discover why my results were worse than other research groups using similar methods on the same datasets, the reason turned out to be that I was using nested cross-validation and hence didn't benefit from the optimistic bias.

G. C. Cawley and N. L. C. Talbot, Over-fitting in model selection and subsequent selection bias in performance evaluation, Journal of Machine Learning Research, 2010. Research, vol. 11, pp. 2079-2107, July 2010. (http://jmlr.org/papers/volume11/cawley10a/cawley10a.pdf)

The reasons for the bias with illustrative examples and experimental evaluation can be found in the paper.