Dye-sublimation is a method by which a colored dye is permanently embedded into material, rather than applying an ink to the surface as in screen printing.
Sublimation is the chemical process wherein a substance moves directly between a solid to a gaseous state without first becoming a liquid. In dye-sublimation colored dye is superheated and then embedded into fabric, where it bonds on the molecular level with polymers (large molecules consisting of repeating simple molecules linked together) in the fabric, so that the dye actually becomes part of the material.
This process only works on artificial fabrics composed of polymers, usually polyester, so dye-sublimation is usually reserved for polyester items like lanyards, ribbons, and mouse pad fabric, though ceramics like coffee mugs are often coated with a thin patina of polymers specifically for accepting dyes. T-shirts can be dye-sublimated, but they must be 100% polyester — the process will not work with cotton.