Suppose we have some random variable we want to predict $Y$ (over a space $B$) and some set of features or predictors in $A$ to make predictions of $Y$ this are sampled from a random variable $X$. You assume there is some relationship between $Y$ and $X$ given by

$$Y = f(X) + \epsilon.$$

Where $\epsilon$ is some Irreducible error within our system and $f: A \rightarrow B$.

Then you normally pick a modelling paradigm, like Linear regression, which relates to a subset of functions from $A$ to $B$, $M \subset Func(A,B)$ with an objective function $O$. Then pick the best $\hat{f} \in M$ with respect to the objective function $O$. Therefore you are making the prediction

$$Y \approx \hat{f}(X).$$