Brown sugar is, quite simply, white sugar that has been flavored and tinted with a bit of molasses. After the white sugar is refined, it’s dissolved and mixed with a molasses syrup concentrate and then recrystallized. A thin film of molasses coats the sugar crystals and contributes to the color, flavor, and moisture of the sugar.
Light brown sugar contains less molasses (about 3-1/2%) than dark brown (6-1/2%), accounting for differences in color and flavor. In general, if a recipe calls for brown sugar, it refers to light brown. Dark brown sugar (also called old-fashioned brown sugar) tends to be reserved primarily for recipes like baked beans, gingerbread, spice cakes, and other dishes where you really want a deep molasses flavor. You might also see granulated brown sugar in the grocery store. It has less molasses than light brown sugar and has been dried so that it doesn’t clump and will pour freely like white sugar.
If a recipe calls for brown sugar and you have none, you might try these substitutions recommended by Rose Levy Beranbaum: For 1 cup of light brown sugar, use 1 cup white sugar plus 1/4 cup molasses. For 1 cup of dark brown sugar, use 1 cup white sugar plus 1/2 cup molasses.