In the context of the Storm Prediction Center's (SPC) Short-Range Ensemble Forecast (SREF), plumes are a way to account for uncertainty in initial conditions and models. The SREF is a system that helps to predict hazardous weather, such as severe convective storms. 
A plume is a column of a substance, such as dust, gas, or liquid, that moves through another substance. Some examples of plumes include: Smoke from a chimney, Steam from a smokestack, Rain clouds, Snow clouds, and Breath.