Evaluation functional
In words...
For a space of real-valued functions over a given domain, the evaluation functional is the functional that, for any function of the space and any point in the domain, outputs the value of the function at that point.
In pictures...
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In maths...
The evaluation functional in a space $\H$ of functions from $\X$ to $\Y$ (i.e., $\H\subseteq \Y^\X$) is the functional defined as
$$
e : \X \times \H \rightarrow \Y
$$
with
$$
\forall \g x \in \X,\ \forall f\in\H,\quad e_{\g x}(f) = f(\g x) .
$$