Sublimation is a phase change process in which a substance is taken directly from a solid to a gaseous state without becoming a liquid in between. One common example of sublimation is dry ice.
Pressure plays a large role in sublimation because it has a direct impact on the temperature at which a substance undergoes a phase change. For example, if the pressure conditions surrounding water get low enough, a triple point occurs, where the substance exist in equal quantities in all three states. Sublimation of water will occur below the triple point. Different substances have different triple points.