Sublimation is the process of going directly from a solid to a gas without passing through the liquid phase. In this case it means that we can print a full-color image using sublimation dyes (rather than ink) onto special sublimation transfer paper, then heat press it onto certain garments and plaque materials. The dye (solid) is then turned into a gas and embedded into the material.
The result is something that will not peel or fade. When used on garments it's the most lightweight method of "printing". Rather than being inks on top of the fabric, it's the fabric itself that has changed color. This allows the maximum amount of air-flow through the fabric.