Following the definition given in your question, the empirical accuracy is the proportion of records correctly predicted by the model.
For example, if you tested your model on 100 records and it correctly predicts 70 of them, then the empirical accuracy is 70 / 100 = 0.7, or 70%.
If the model has a true accuracy of $p$ (i.e. in the long run it correctly predicts a proportion $p$ of all records) then there is a probability $p$ that any individual record will be correctly predicted. You can think of the prediction of record $i$ as a random variable $X_i$ which takes the value 1 with probability $p$, and 0 with probability $1-p$.
If you are testing $N$ records, then each one individually has probability $p$ of being correctly predicted, then the total number of records correctly predicted is
$X = \sum_{i=1}^N X_i$
which is itself a random variable. Being the sum of $N$ identically distributed Bernoulli random variables, the distribution is known to be Binomial(N,p). This distribution has mean $Np$ and variance $Np(1-p)$, as the book describes.
The empirical accuracy is the proportion of records predicted correctly, i.e. it is given by
${\rm acc} = X/N$
Here $N$ is just a constant, and we use the following rules which apply to any random variable $X$ (subject to a couple of technical conditions you don't need to worry about):
- ${\rm E}(cX) = c{\rm E}(X)$
- ${\rm Var}(cX) = c^2{\rm Var}(X)$
Here ${\rm E}(X)$ is the expectation or mean of $X$, and ${\rm Var}(X)$ is the variance of $X$.
We have multiplied $X$ by $1/N$ to get acc, so the mean of acc is $(1/N) \times Np = p$ and the variance of acc is $(1/N)^2 \times Np(1-p) = p(1-p)/N$ as claimed in your book.