The brown sugar that is sold in grocery stores is a mixture of refined, white sugar and molasses syrup. It has a soft, moist texture and delicate molasses flavor. Unless a recipe specifically indicates otherwise, it is generally fine to substitute one for the other, though you will notice a slight difference in color and flavor. You can also substitute a cup of firmly packed brown sugar for a cup of granulated sugar. Keep in mind, however, that in baked goods this will typically yield a moister, chewier result than expected, since brown sugar absorbs moisture from the air more than granulated sugar does.
Many recipes call for a combination of sugars to produce the desired flavor and texture.