I read this at sixteen and took away that it was about clever self-reference. Reading it again at twenty, it is about something much narrower and more interesting: what it takes for a formal system to talk about itself, and what breaks when it does.
The dialogues, which I found tedious the first time, are doing real work. They introduce every structural idea informally before the chapter states it, so by the time you meet the formal version you have already had the intuition for twenty pages.