Claire asks via twitter:
This recipe orginally comes from the very impressive Modernist Cuisine. Sadly, I don't have the spare money to get a copy of Modernist Cuisine right now*, and none of my local libraries carry it. Perhaps I'll buy it one day. So if someone who has it writes in and says that I got it all wrong, I'll accept blame. That being said, it looks to be fairly simple, if awfully clever, so I'm willing to take a stab at it.
A normal panna cotta is essentially milk gelatin. Instead of a normal cherry or lime gelatin dessert made with water and flavoring, and perhaps bits of fruit, a panna cotta is just milk, flavoring, and gelatin made with the same method. People are finicky about the exact amount of gelatin to use, and there are rather lurid descriptions of exactly how much jiggle a panna cotta should have, but, overall, it's fancy Jell-O™.
When you say "citric acid + milk", most people think cheese. Ricotta cheese, especially, as it's one of the easiest cheeses to make, and much better fresh than what you get at the store. In any case, acid such as lemon juice or citric acid causes milk to curdle, which is fantastic if you want to separate the whey from the rest of the milk and turn it into cheese. The same process causes yogurt, crème fraiche, and sour cream to be a thickened version of a milky substance, each with different properties based on how much fat, how many milk proteins, and how acidic the mixture was.
Now, your typical ricotta will call for something like 2 tablespoons of lemon juice to 2 quarts of milk plus one cup of cream. This recipe calls for 1 quart of heavy cream to 1 tablespoon of vinegar and 1/2 teaspoon of citric acid. Thus we have significantly more fat than liquid, which makes sense because we don't want the liquid and whey to separate from the mixture, we want one gelatinous mass. More importantly, though, cream has very little protein in it compared to milk. It's the acid denaturing the proteins that causes the milk to curdle and thicken, so a small number of proteins will cause a general thickening, while a large number of proteins will cause a big separation between curds and whey.
The other difference between making cheese and this panna cotta recipe is the 1/2 cup of sugar. Now, most of that is for flavoring, I'm sure, but I think some of it is also to tie up the water. As we've discussed before, sugar and water love each other very much, and any chance that they have to canoodle, they will take, which probably helps keep the liquid integrated into the rest of the dish. Not much, because a crème fraiche is essentially the same product without the sugar, and it doesn't separate, but I would be surprised if there weren't some effect.
*-For those who don't know about it, Modernist Cuisine is a $500 set of books that is meant to explain pretty much everything we know about home and restaurant style cooking nowadays, from roasting to techniques that have been pioneered in the last decade.