What is the most important aspect of a story's structure?

Understanding purpose of said structure. It serves as scaffolding for your story to hold it taut. It allows writter to understand and fullfill readers expectations (think midpoint twist - reader expects change here or will get bored), control pacing and keep track where writting is supposed to go.

When you think about western strory structure you can clearly see points of change and intervals between them.

Story begins => Tension rising => Change! (Disruption of Status Quo, Inciting Incident, other names possible too) => Consequences of Change => Change becomes permanent (1st plot point) => Tension rising => Change! (Midpoint Twist) => Consequences of Change => Change becomes permanent (2nd plot point) => Tension rising => Change! (Climax) => Tension decreasing towards end => Possible but not necessary Change at the end (Final Twist)