The Partagas factory. Like most, this now makes a number of other brands including Romeo and Juliettas.
Cuba leads the market in cigars by a vast margin, although in fact a number of the big brands manufacture non-cuban versions on other Caribbean islands so that they can be imported into the US. Regardless of where they are made, the best cigars are hand-rolled from whole leaves. A bunch of three or four leaves scrunched and twisted together and then tightly wrapped in another leaf makes up the main body of the cigar, and it is the mix of leaves chosen that defines the flavour and is the major difference between brands. Around this rough tube, another leaf is painstakingly wrapped to create the proper shape and the smooth, even, outside of the cigar. Being able to form the correct length, width and shape for the cigar brand at this stage is the result of a training course that takes several months, with brands that feature unusual shapes, such as the torpedo, requiring particular care. Over the course of this training, hundred of cigars are produced that may be perfectly serviceable, but are not good enough to be sold. These are used to make up the part of the workers' pay that consists of three cigars a day. Others, which may be close to perfect, are sometimes smuggled out and packed in forged or stolen boxes, and it may occasionally be these that you will end up buying if you try to get a bargain by purchasing cigars on the street.
I'm not sure where the strange legend comes from that Cuban cigars are rolled on the thighs of virgins. In fact, at least in the Partagas factory, they are rolled on neat rows of wooden tables, by men and women proud of a job that is skilled, prestigious, and well-paid by local standards.
The resulting cigars are pressed, trimmed and ultimately boxed and shipped out. Cigars are boxed to try to get as little variation in colour within a box as possible, and spot checks are done to ensure that the quality and consistency remains high. It is, all in all, a remarkable process and the care that goes into a handmade cigar is reflected in the enjoyment you get from it.
Cheaper cigars are machine made, and the filler is made from chopped tobacco leaf, rather than whole leaves. Often, it is the discards from one of the hand-made cigar factories that are then bundled up and sent off to make machine-made cigars, or even the strong cuban cigarettes that, for some reason, don't seem to have caught on elsewhere.
Cigars must be stored in a humidor to keep them at their best. An even temperature and humidity is important and, while preferences vary, most people agree on something around 70F and 70% humidity. The climate of the tobacco-producing areas of Cuba is remarkably close to this for much of the year, which is probably an indicator of why it makes the best cigars in the world.