Dye Sublimation printing is a process where a digital image is first produced through the use of computer graphic software. Then this image is printed onto a coated media using a set of special heat-activated inks. Finally, it's then transferred to the final product using heat transfer equipment.
When heat is applied to the printed coated sheet, the ink sublimates (is absorbed) into the surface of the final product. This is like a tattoo, where the final
image is not affixed to the receiving surface (like silk-screening, hot-stamping, and printing), but is absorbed into it; in effect becoming part of the material.
In printing the biggest difference between it and other types of printing is 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. This makes the image look less like it was made up of little dots. It also is typically less vulnerable to fading and distortion over time.
If you looked inside a dye-sublimation printer, you would typically 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.
I am also told that the Phaser line of Techtronix dye sublimation printers uses a very waxy media that comes in large chunks that are fed into a hopper, rather like putting cheese in a cheese grater.