Brown sugar is a soft sugar whose crystals are covered by a film of refined molasses. Light brown sugar and dark brown sugar vary in their amounts of molasses - therefore, dark brown sugar has a deeper molasses taste than light brown.
Brown sugar is produced similarly to white sugar, with two exceptions. The crystals are left much smaller than for white sugar, and the syrup or molasses is not washed off completely. Some brown sugar producers produce brown sugar by adding molasses to completely refined white sugar crystals in order to more carefully control the ratio of molasses to sugar crystals.
This is mainly done for inventory control and convenience; there may also be tax-related reasons to use sugar from sugar beets with molasses from sugar cane. The resulting brown sugar is not any different, whichever way it is prepared