I *think* persuasion works like so:
First you have to have some threshold in a stat to get the option to even show up in dialog. That's just in the stat, though - I don't think persuasion counts for anything at that point. The persuasion stat comes in when you pick one of those options. Each one will have a threshold assigned, from 0 to 99. If you've got that level of persuasion then you get the success. If not you get the fail.
So say you walk up to some giant and want him to do something he doesn't really want to do. You get some standard options, an option based on strength to threaten the giant with a pummeling, and an option based on wits to that the squirrels are plotting against him and he needs to go check it out. The strength option will need a ridiculous persuasion - what are you going to do, punch it in the shin? The wits option might work on a dumber giant, though. If it were a frail old wizard, the strength option would probably have a lower threshold than the wits.
Do NOT discount the other options, though! This is not the kind of game where, if you see a tag, you know that's likely to be the best option. There could be an option with no tag and no requirement for information from some previous questing that works quite well.
The options (and tags like Jester) can open up some nice roleplaying. If you're playing a punch-first-think-later fighter, he might well threaten to punch a giant in the shin.