Mac storage basics · Library folders explained
What is the Saved Application State folder?
Short answer: It's where macOS remembers each app's open windows so they reopen later. It's usually small; deleting an app's entry only stops its old windows reopening.
It's where macOS remembers which windows each app had open, so they can come back when you reopen the app or restart with Reopen windows when logging back in ticked.
It's normally small and harmless. Deleting an app's folder there only means its windows won't reopen as they were last time; it frees little space. It's sometimes worth clearing for one app that keeps reopening a broken window — quit that app first.