I haveen't read that book, but I'll try to answer anyway from a pure statistics point of view.
You assume a model and some random variables or a stochastic process which models the part of reality you are interested in, i.e. the value of a stock or its return in time. If the model is true this stochastic process is assumed to have generated the data you can observe and the task at hand is to estimate certain proberties of the stochastic process.
I assume with standard derivation Sinclair means the empirical standard derivation, which is an estimator of the theoretical standard derivation, i.e. the true volatility in the model. This is along the same lines as the mean of a sample
is an estimator for the expected value of the theoretical quantity that generated your sample, according to your model.