In his book, Bishop starts of with easy examples involving a few random variables and subsequently becomes more and more general as the chapters progess, until, finally, all quantities become random variables.
In the context at hand, both quantities, the regressors/features $x$ and the target $t$ are stochastic.
Therefore, there exists uncertainty in both, the values of the regressors/features and those of the target given the regressors. This becomes all the more apparent, if the joint probability distribution $p(x,t)$ is decomposed into $$p(x,t) = p(t|x)p(x)$$ using Bayes' rule.
Clearly, the goal of learning is to minimize the expected error stemming from both sources, the uncertainty of the features and the target alike.
Classical regression only considers modeling the $p(t|x)$ part and assumes the $x$s are given (or equivalently that p(x) is given by an empirical distribution consisting of a sum of dirac-delta distributions). In a more general setup however one may head for a generative model for the $x$s as well, which involves the modeling of $p(x)$. Therefore, the formula in question is general enough to allow for both types of modeling.