Persuasion has been a dialogue element in many popular Bethesda games, with Starfield taking the established system and adding a bit more to it. When offered, Persuasion allows players to talk their way into or out of situations they wouldn't normally be able to.
Starfield: How Persuasion Works
Persuasion takes a bit more than selecting a single dialogue option in Starfield; here’s how the new system works.