In American recipes, this is commonly referred to as a 'wash' or specifically an 'egg wash.' We've heard this term used interchangeably as a noun ("...apply the dorure...") and as a verb ("...next, dorure the surface..."), though the French can feel free to correct us on this one!
In French, 'dorure' literally means 'gilding.' We suspect this refers to both the process of coating the surface and also the color of the final product. When we apply a dorure to shaped breads, rolls, or pastries, the goal is to paint the surface of our soon-to-be goodie with a very thin coating. This coating won't have any noticeable flavor, but it will help give your baking a rich golden color and a nice shine. If you want to sprinkle textured sugar or seeds over the top, dorure will also help everything stick in place.
The most common kind of dorure is a simple wash of one egg and one tablespoon of water, like in the recipe for no-knead challah from Artisan Bread in Five Minutes a Day. You can also use just the yolk with a tablespoon of water, or just the egg white by itself. (The water helps to thin out the yolk and make it easier to brush on.) Dorure can also be milk or melted butter, also thinned with water if desired.
Apply the dorure right before you put your baking in the oven, and it's easiest if you use a pastry brush. Shake off any excess and go for a thin even layer--especially around any folds or corners. Be careful of puddles or drips since those areas will brown faster.
Finally, whenever you use a dorure, remember to check on your baking frequently to make sure it's not getting too browned. If it starts to scorch, cover the top with a piece of aluminum foil.