If you looked inside a dye-sublimation printer, you would see a long roll of transparent film that resembles sheets of red, blue, yellow, and gray colored cellophane stuck together end to end. Embedded in this film are solid dyes corresponding to the four basic colors used in printing: cyan, magenta, yellow and black. The print head heats up as it passes over the film, causing the dyes to vaporize and permeate the glossy surface of the paper before they return to solid form.
So the main difference between this and other types of printing has to do with heat. The vaporized colors permeate the surface of the paper, creating a gentle gradation at the edges of each pixel, instead of the conspicuous border between dye and paper produced by inkjets. And because the color infuses the paper, it is also less vulnerable to fading and distortion over time.
A dye-sublimation printer (or dye-sub printer) is a computer printer which employs a printing process that uses heat to transfer dye to a medium such as a plastic card, printer paper or poster paper. The process is usually to lay one color at a time using a ribbon that has color panels. Most dye-sublimation printers use CMYO colors which differs from the more recognized CMYK colors in that the black dye is eliminated in favour of a clear overcoating. This overcoating (which has numerous names depending on the manufacturer) is effectively a thin laminate which protects the print from discoloration from UV light and the air while also rendering the print water-resistant. Many consumer and professional dye-sublimation printers are designed and used for producing photographic prints.
Sublimation is when a substance transitions between the solid and gas states without going through a liquid stage; dry ice is an example. In a dye-sublimation printer the printing dye is heated up until it turns into a gas, at which point it diffuses onto the printing media and solidifies. Prior to printing, the dye is stored on a cellophane ribbon. The ribbon is made up of three colored panels (cyan, magenta, and yellow) and one clear panel which holds the lamination material for the overcoating. Each colored panel is the size of the media that is being printed on; for example, a 6" by 4" dye sub printer would have four 6" by 4" panels. During the printing cycle, the printer rollers will move the media and one of the colored panels together under a thermal printing head, which is usually the same width as the shorter dimension of the print media. Tiny heating elements on the head change temperature rapidly, laying different amounts of dye depending on the amount of heat applied. After the printer finishes covering the media in one color, it winds the ribbon on to the next color panel and partially ejects the media from the printer to prepare for the next cycle. The entire process is repeated four times in total: the first three lay the colors onto the media to form a complete image, while the last one lays the laminate over top. This layer protects the dye from resublimating when handled or exposed to warm conditions.
source: http://en.wikipedia.org/wiki/Dye-sublimation_printer