Let $S = \{x_1, x_2 \ldots x_n\}$ be a set of $n$ points in $\mathbb{R}^d$, then how can one geometrically interpret or visualise the affine hull of $S$?
It is somewhat straightforward to think about the convex hull intuitively, but unable to get any geometric interpretation for affine hull especially when the $|S|$ exceeds the dimension of the space $\mathbb{R}^d$.
If $S=\{x_0\}\sqcup T$, then the affine hull of $S$ is $$x_0+\operatorname{span}(T-x_0)$$ where $T-x_0=\{t-x_0:t\in T\}$ and $\operatorname{span}$ refers to the linear subspace generated by that set.
If you aren't sure why the formula I gave is the affine span, then proving from the definitions that it is so is a good exercise.