DPVA stands for Differential Positive Vorticity Advection. One way to understand what this is can be done by breaking down and defining each of the four terms that make up DPVA. The word positive is in reference to "higher values". Higher values of VA are moving toward the forecast region. Differential refers to "a change in the vertical". VA is changing from the low levels of the troposphere to the upper levels of the troposphere. RULE OF THUMB: vorticity will generally increase from the surface to 500 millibars. Vorticity advection is usually higher at 500 millibars than in the low levels of the troposphere because the wind speeds tend to increase with height (500 millibar winds near a trough will often be stronger than low-level winds). Because of this general rule, the "D" is often left out. Then what is left is PVA (positive vorticity advection). Vorticity is any twisting motion in the troposphere.
Positive vorticity can be broken down into three components, which are positive shear vorticity, positive curvature vorticity and earth vorticity. A counterclockwise spin in the Northern Hemisphere will produce positive vorticity. Since the earth spins counterclockwise, earth vorticity is always positive. Motion within a trough produces positive curvature vorticity (because air is rotating counterclockwise within a trough). Wind speed increasing away from a point source will produce positive shear vorticity. Positive shear vorticity is also common in a trough since the highest winds are often located away from the center of the trough.
Vorticity maximums are located in regions where there is high positive shear vorticity co-located with positive curvature vorticity. Again, this is most common just to the south of the center of a trough. The speed of the winds and the amplification of the trough will determine the positive vorticity it will generate. The last term "A" means the DPV is moving from one place to another over time. Wind speed and the orientation of the lines of constant vorticity to the height contours determines the rate at which vorticity advection will take place.
Putting this all together, DPVA means: positive vorticity increasing from the surface to the upper levels is being advected. DPVA causes the troposphere to become more dynamically unstable. DPVA occurs in shortwaves and within just about any trough. DPVA contributes to rising air. The spin up of vorticity causes the troposphere to cool since rising air cools. This cooling will lower heights aloft. Cooling the middle and upper levels of the troposphere causes the troposphere to become more unstable. DPVA is associated with upper level divergence and rising air. DPVA along with low level warm air advection is a favorable environment for precipitation and storms.