How can this open map characterization be explained or interpreted?

I hope you're having a good day.I'm an undergrad mathematics student, I took a general topology course a few months ago, and I'm now reviewing topological spaces to prepare for functional analysis.I remember coming across the following proposition during the course:Let $X$ and $Y$ be two topological spaces, and let $f$ be a map from $X$ to $Y$. The following statements are equivalant.
(i) $f$ is an open map.
(ii) For all subsets $B$ of $Y$, and for all closed sets $F$ of $X$ such that $f^{-1}(B) \subseteq F$, there exists a closed set $D$ of $Y$ such that $ B \subseteq D $ and $ f^{-1}(D) \subseteq F$.
I understand the proof of this proposition, however, I never quite got why it's important, or how it's useful, there's even another proposition analogous to this one for closed maps, and I don't understand it either. I really appreciate it if anyone could explain the importance/implications of this proposition, and if it relates to any other important result. Thank you.