Ok. To a certain extent this is supposition, because we don't have the full chapter. But its relatively informed supposition, hopefully free from hysteria.
The party needs to accomplish something non combat related, that's likely to take more than a single skill check to complete. Lets say its convincing the Duke to redistribute his troops away from one border and closer to another.
You, the DM, declare that a skill challenge is taking place. You set a general challenge rating, which is sort of your default Skill DC for when the rules don't otherwise dictate a particular DC. Lets say you set it at 15. This is now your touch stone DC for the encounter. This is particularly useful when the PCs are using skills in an "opposed roll" type situation when the skills themselves aren't really opposed roll type skills. For example, climbing a wall faster than someone else. Climbing isn't usually an opposed skill, its a fixed DC. But in a skill challenge it might be best, based on story needs, to define it otherwise.
The PCs may then use skills to try to get closer to completing the challenge.
So PC1 comes up with an idea on how to use his Intimidate skill to help in the skill challenge. You set a DC for this skill check based on how likely you think this skill is to work, as per standard. You take into account all the usual stuff- what leverage do the PCs have to help them intimidate the Duke? You are permitted to declare that the PCs simply lack the ability to intimidate this particular character, for story reasons, as standard. Then the PC rolls his skill roll. As usual, you can assign bonuses for good roleplaying, or whatever it is you do with social skill rolls.
If you think that PC1s idea makes sense, and he beats the DC, the party gets a "success."
If you think that PC1s idea doesn't make sense, and he beats the DC, perhaps it doesn't give the party a success, but it doesn't hurt.
If you think that PC1s idea is likely to be counterproductive, or if he fails the skill roll, the party gets a failure.
Once the party gets a certain number of successes, they succeed at their overall objective.
If before that happens they get a certain number of failures, they fail.
That's... pretty much it.
It doesn't negate any of the usual rules about narration and DMing, but it does present a framework for you as a DM to prepare in advance for scenes that are likely to be resolved by using skills.