Letterpress is a centuries old printing process in which a reversed, inked surface is pressed onto paper resulting in a right-reading print. Originally metal/wood type or etched metal plates were used, but now it is more common for designs to be computer generated and made into a plastic printing plate. For many centuries letterpress was the only form of printing, but it was largely replaced in the last hundred years by offset and then digital printing. Letterpress has recently had a bit of a renaissance as it offers a different tactile experience to flat-printed items, and has gained popularity for specialist items like business cards and wedding stationery.
While any paper can be used for letterpress printing, most often a high-quality thick, soft paper (often made from cotton) is used that really shows off the impression that is made when plate meets paper. If you are interested in learning more, visit the following websites for more in depth information: Wikipedia on letterpress printing; British Letterpress; Five Roses Introduction to letterpress printing; Briar Press (great forum full of information).