Lambda Calculus Notation
It probably depends on what $\mathcal{F}$ is -- the text tells you.
Each $f\in\mathcal{F}$ is a build-in/primitive function (such as $+$) and [pur7] gives the result of applying it to some arguments. $[\![ f]\!]$ gives the semantic interpretation of the function, and applying that to the arguments $v_1,\ldots,v_n$ gives the result of the function.