Rapadura is a trendy name for pure cane sugar.
Rapadura or raspadura is a traditional Brazilian word for the result of the first distillation of cane juice after it is extracted from the sugar cane; after having the excess water evaporated over low heat, but before the molasses has been separated out. It literally means something like 'hard scrapings', and is normally considered an unfinished product. It has gained popularity in the organic and raw food movements. Rapadura was registered by the German Rapunzel company as a trademark for their organic sugar, but this did not fly well in Brazil, and they eventually dropped their claim to a trademark -- but not their use of the term. Rapadura is now often found in ingredient lists of organic foods from many companies. Use of the term rapadura gives no definite implications as to point of origin, although there is the suggestion that it comes from South America, particularly Brazil or the Dominican Republic.
Raw cane sugar contains traces of vitamins and minerals naturally present in the sugar cane, including polyphenols, that would normally be removed with the molasses. While these are good nutrients, you should not be eating enough sugar for this to be a significant source. If you are interested in gaining more of these nutrients, you may also want to look into using molasses.
Other names for the same substance include Panela (from Central and Latin America), Chancaca (Peru, Bolivia, and Chile), Piloncillo (Mexico), Jaggery (India), and Sucanat (a US trade name for a slightly more processed product, in which the molasses is removed and then added back in), and dried cane syrup.
Rapadura is also a common name for types of candy made from dried cane syrup, akin to toffee. This sort of treat is common in many parts of the world, but is hard to find in the US.