Vorticity is the localized rotation of the air. Air that rotates counterclockwise, such as in cyclones and troughs, is said to have positive vorticity. Clockwise rotating air, such as in high pressure systems and ridges, has negative vorticity. The advection of vorticity at high levels will result in a response at the surface which will attempt to offset the effects of the advection. More specifically, vorticity advection is indicative of rising motion/falling pressures at the surface. For example, look at this 500 mb map for 12Z, October 29, 1995.