In Ye Olden Days when sugar cane was about the only viable source for bulk sugar, cane was pressed for juice and the juice was reduced down to syrup. The syrup was crystallized and the crystalline product spun in a centrifuge to remove remaining liquid (molasses). The leftover crystals can be dried and ground into raw (brown) sugar or rinsed to wash out the remaining impurities to produce white sugar. Current production methods are still basically the same steps but the process has been streamlined and automated significantly.
Back in the 80's I had a chance to see the process demonstrated in a vintage Hawaiian sugar factory. The factories were hot, humid hellholes for workers in the day but the process was way interesting to watch.
Also interesting to note that people willingly pay a premium for raw sugar, once considered an inferior product.
Back to the OP... my grandmother would use a dollop of sorghum syrup or molasses combined with plain table sugar. Easier to keep than a bag of brown sugar (which, unless used up quickly, turns into a sweet-smelling brown brick).
Brad