Each crystal of brown sugar is coated with a thin layer of molasses. When the sugar is fresh, this film makes the sugar crystals slip easily over each other and the brown sugar as a whole is soft and malleable.
If the brown sugar is left exposed to air, the moisture in that coating of molasses will evaporate. Individual particles of sugar literally become glued to each other as the film between them dries out and the brown sugar hardens into a solid mass.
Ironically, this molasses is also very hygroscopic, meaning it readily absorbs moisture. That's why when you seal a piece of bread or a dampened sugar saver in with the sugar, it becomes soft again. The molasses literally sucks in the moisture.
Good to know!