Crème fraîche is similar to sour cream, but I think it has a nicer mouth-feel, and has a wider variety of applications. It has a sour note, but it also a hint of nuts. It can be whipped to create a light structure. It can be used in savory or sweet sides of the kitchen. I've seen it flavored with fruits, curries, and more. You can make dressings for salads or other vegetables with this, as it is a nice base for remoulade. It is also a great way to add richness to meat and fish sauces. This will keep for a week to two weeks in the fridge.
Let the cream sit on a counter to at room temperature for 24 hours. It will become thicker and start to develop some of its characteristic sourness. It will continue to thicken and develop flavor as it sits in the fridge. You can see that it is much thicker than cream.
In More Depth
The fat in milk comes in the form of tiny globules. Whole milk contains ~3.5% fat, while heavy cream contains upwards of 35%. This makes cream better able to be whipped, resist curdling when heated, and gives it its characteristic mouth coating goodness. The important thing to understand is that milk is a colloid, an emulsion of fat in water, held together with proteins. You may know that raw milk will separate, the cream rising to the top. Homogenized milk has been forced through a fine strainer at high pressure, breaking up the fat into smaller bits so they are more easily held in suspension. Too much heat or acid and the emulsion will break.
I have often in the past tried using milk based products in making warm and hot sauces, but found that the fat and solids would separate, making a greasy and unappetizing appearance. What I was seeing were the proteins of the milk coagulating into a tight structure which releases the fat and whey. With heavy cream, and by extension crème fraîche, there is enough fat that the milk proteins are trapped, unable to curdle. Sour cream will curdle with heat, as will milk and yogurt. The reason for sour cream and yogurt is that their acidity already puts them on the edge, the heat easily pushing them to curdle. More on acid below, under Culture.
The globules of fat also have a role to play when cream is whipped. The mechanical action of whipping breaks up the globules into ever finer structures, which then can form into rings of condensed fat trapping air bubbles. If you continue whipping you break the globules and release the fat molecules, which will begin to coalesce into ever increasing sizes, producing butter. Ice cream also illustrates the role of fat globules. Like whipped cream, the fat stabilizes air bubbles produced when you churn the cream. As a side note, ice cream is very interesting stuff with a lot to explore: the controlled crystallization of sugar and water, thermoreversability through the use of stabilizers, and tastes, all could be subjects in future posts.
You can make harder whipped creams by reducing the water content/increasing fat content (heat the cream to cook off some water), then chilling before whipping. To make softer whipped cream, add a bit of milk. To aid quicker whipping, add a touch of acid (lemon, a dash of tartaric acid, etc). This helps to separate the fat from the proteins. That said, the amount of fat globules and the mechanical action of breaking them up is the key.
Milk fermentation. Milk contains water, proteins, fat, and sugars (lactose). It is this last molecule that makes fermented milk products possible. The lactose serves as a food source for bacteria, which produce lactic acid, preserving the milk. There are literally hundreds of different kinds of fermented fresh milks. Each relies on a set of microbes to digest the sugars and acidify the milk.
Kept at moderate to warm temperatures, the microbes multiply rapidly and the process accelerates. The acidic conditions produced by these helpful bacteria create an environment unfriendly to disease causing bacteria. The acid also causes the proteins to get tangled up with each other, creating a gel structure which thickens the end result. With yogurt and fromage blanc, the process is much quicker (yogurt can gel in a matter of hours, fromage blanc even faster). The faster gelification of yogurt and cheeses produces a looser gel structure, which leaks whey and leaves behind the curds. The slower process involved with crème fraîche creates a denser network of proteins, which retains the whey.
There's a lot going on, even in the ostensibly simplest substances. We can easily take advantage of these complex processes to produce delicious results with very little cost. I can only speak for myself, but I think knowing a little bit about what is going on to produce these foods increases my appreciation for them and helps me understand how to use them effectively in the kitchen.
Richard Feynman in What Do You Care What Other People Think? (1988)
I have a friend who's an artist, and he sometimes takes a view which I don't agree with. He'll hold up a flower and say, "Look how beautiful it is," and I'll agree. But then he'll say, "I, as an artist, can see how beautiful a flower is. But you, as a scientist, take it all apart and it becomes dull." I think he's kind of nutty. [...] There are all kinds of interesting questions that come from a knowledge of science, which only adds to the excitement and mystery and awe of a flower. It only adds. I don't understand how it subtracts.
The above adapted from my reading of McGee. Any errors are my own.