Sorry Dena, but sublimation is the process in which solid is changed directly to gas. Deposition is the process that changes gas directly to solid. Melting is solid to liquid and freezing is liquid to solid.
Now back to the subject. Dye Sublimation is a process of instead of using liquid ink, the ink is solid on a piece of plastic film. When printing, the print head passes on top of the corresponding color and vaporizes the ink. Then the gaseous ink passes onto the glossy paper before it soldifies again. This process is repeated for each of the 4 colors, cyan, magenta, yellow, and black. The mixing of any two/three/four will create other colors. Because the printing is layering process (one color on top the other), you will actually be able to "feel" and see contours of the details of the photo on the paper after printing.
Now the reason the printing style is good is because there are no pixels. Its a continuous shade of color much like photos from regular film cameras. Also since there is not real dying process, the print-outs do not fade. The only drawback is that its terribly slow and its expensive to buy the consumables (The ink is packaged with the paper).
What model, make, and brand of printer do you own (primary printer), and are you happy with it?
Brother
Canon
Dell
Epson
HP
Lexmark
Samsung
Sharp
Other (which one?)

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic