A paradox is an apparent contradiction which turns out to be true. For example, the Bible says in order to be a king one must become a servant, and in order to become rich one must first be poor. Both of these statements appear to be contradictions; however, they are truthful in their meaning, if not in their form. In this quote from The Great Gatsby, Jordan uses a paradox to comment on how much unexpected privacy there is in a large gathering--because one can easily get lost in a crowd, deliberately or not, and no one would notice--thus the intimacy. In a small, more traditionally intimate gathering, everyone notices everyone, and all actions are inevitably scrutinized--or at least noticed. No privacy. She's right, of course, but her words don't seem to be true, logically:
"And I like large parties. They're so intimate. At small parties there isn't any privacy."
We typically think of small parties as being intimate and large parties as being personal. This kind of reversal is what makes a paradox work.
A paradox is an apparent contradiction that is actually true. In this case, one would not expect the speaker to say large parties are intimate. Most of us would associate large parties with a sense of anonymity and shallowness, in that there would be too many people to develop any kind of intimacy. But here the speaker is saying the opposite. In this case, small parties offer no privacy, but at a large party one can slip away unnoticed for wanted intimacy. At a small party, people are essentially forced to interact and everyone is exposed. But at a large party, smaller groups and pairs can have the privacy they desire.