Not to be confused with turbinado or "raw" sugar (which is brown because it is unprocessed), light brown sugar and dark brown sugar are made by simply adding molasses to refined (white) sugar. As you might suspect, dark brown sugar has more molasses in it than light. You can use the two varieties interchangeably in most recipes, depending on the kind of flavor you're craving. Light brown sugar is delicate, while dark brown has a stronger, more intense molasses flavor.
If you don't have brown sugar in your pantry, you can actually make your own. Combine the following ingredients and whiz away in a food processor (or mix vigorously by hand):
1 cup granulated white sugar + 1 1/2 tablespoons molasses = Light Brown Sugar
1 cup granulated white sugar + 3 tablespoons molasses = Dark Brown Sugar
Storing brown sugar is trickier than plain old granulated sugar. Once it's exposed to the air, it will clump up and become hard and brick-like. You can use common sense to prevent this by sealing it in an air-tight container, but all is not lost if you find yourself facing a sugar brick: just pop it in the microwave with a (microwave-safe!) bowl of water and nuke it for 30 seconds at a time until soft.