Example: (for those who haven't played Fallout 3)
Quest: You need a key from a person who won't hand it to you.
You can eaither tell him:
[Strength] Give me the damn key or I'll ripp you head off!
[Intelligense] You can save us from death if you give me the key.
Will you give me that key?
This is another example of what Kovacius was describing.
You reach a "magic number" in your skill and a new, instantly-successful option appears.
It's an improvement over Oblivion, but Morrowind still did it best.
Your chance to successfully persuade is always there, but it becomes slightly bigger with each skill increase.