You may run across this term in a NWS forecast discussion. Omega forcing deals with synoptic scale rising or sinking of air. The two terms in the omega equation that deal with vertical motion are thermal advection and positive differential vorticity advection. Thermal advection can be either cold air advection or warm air advection.
Cold air advection in the low levels of the atmosphere causes sinking while warm air advection in the low levels of the atmosphere causes rising air. PDVA causes rising air while NDVA causes sinking air. PDVA means higher values of positive vorticity are being advected and that vorticity is increasing with height. A vort max will usually have vorticity increasing with height since winds in the upper levels are generally stronger than low-level winds. The omega equation takes into account the magnitude of sinking or rising due to thermal advection and couples that with the magnitude of sinking or rising due to PDVA or NDVA and determines if the resultant vertical motion is upwards or downwards.
Upward motion implies a greater chance for: increasing RH through a large depth of the atmosphere, clouds, and precipitation. The closeness of the air to saturation and the amount of uplift can be used to forecast clouds, forecast precipitation, and forecast precipitation amounts.