Brown sugar is white sugar with some of the molasses added back in. Raw sugar is naturally brown (and called unrefined or natural brown sugar); during the refining process, the molasses in the sugar is spun off into a separate product (molasses is considered a by-product of sugar refining). Substituting brown sugar for white sugar in recipes adds moisture and a hint of caramel flavor. Brown sugar is moist, and when the moisture evaporates it will harden.
It can be kept in the refrigerator; or else in an airtight jar. If it hardens, it can be softened in the microwave, or by the old-fashioned technique of adding an apple wedge to the bag and waiting a few days for the sugar to soften.