Crème fraîche, as the name suggests, is a French invention, a matured, thickened cream with a slightly tangy, vaguely nutty flavour and velvety texture. It can be as thick as commercial sour cream or almost solid in France. In its homeland, it's made from unpasteurized cream, which already contains the bacteria necessary to thicken it naturally, but the sale of unpasteurized dairy products is illegal in North America. (Seriously. I can buy unpasteurized milk, but I have to meet the dairy farmer surreptitiously in a parking lot and furtively exchange the product. We're both liable for prosecution for this. Ah the excesses the state gets into in the name of public safety!)
Don't fear, however; you don't have to risk arrest to get a reasonable facsimile of crème fraîche. The fermenting agents necessary to make crème fraîche can be obtained by adding commercial buttermilk or sour cream to heavy cream. 35% MF whipping cream works best, giving a thick creamy texture, but as I can get organic cream at 18% MF in the supermarket, I sometimes use that instead. The resulting product is not as thick and tends to accumulate a bit of whey, but I just pour that off.
All you have to do is combine 1 cup (240 ml) cream and 2 tbslp (30 ml) buttermilk or sour cream in a clean container, cover loosely, and let stand at room temperature for 8 to 24 hours, until very thick, like yogurt. Cover and refrigerate for up to 10 days.
As the good DTower says, it's a good addition to sauces or soups, the reason being that, unlike sour cream, it can be boiled without curdling. Or try spooning it over fresh fruit or any dessert for an extra-luscious treat. Yum.