Light and dark brown sugar have different amounts of molasses in them. Molasses is a by-product of the sugar making process. When brown sugar is made, it is first refined into white sugar and then a small amount of the molasses is added back into the sugar to give it a soft or strong molasses flavor.
You can swap light brown sugar for dark brown sugar, and vice versa. The only change will be in the flavor of the item your are baking.