Dynamic overpressure is, to put things baldly,
wind. However, used in its typical context (that of the
effects of nuclear weapons) then it's better described as
God's Own Wind after a day of Heavenly Mexican Food - plus TURBO! (Heh. Sorry.)
After a nuclear detonation, the immediate burst of X-Rays will heat the immediately surrounding atmosphere to the point of saturation, turning it to plasma. As is the wont of (nearly) all things hotter than they were, the atmosphere will want to expand, and it will do so violently.
The outer edge of the blast wave from the detonation will be a hypercompressed 'shell' of air that is moving at speeds above Mach 1, pushed by the continued flood of energy from the blast. The air in this shell is pressurized, and its passage over an object is referred to as static overpressure. However, once it has passed, there is a steady flow of air rushing away from the explosion, and this moving air exerts a force called dynamic overpressure. The first phase, where it flows away from the blast, is called positive dynamic overpressure. This is what makes those wood-frame houses in popular nuclear test films blow over backwards.
Immediately after this, however, there is a reversal. All the air which has been (super)heated by the blast moves upwards to form the mushroom cloud. This, coupled with the area where the air has been blown outwards, leaves a low-pressure zone. Air rushes back in from the surrounding areas to equalize pressure; this flow is typically several times stronger than most natural winds. As a result, in some of those test films, you can see house rubble, trees, etc. pause in their flight and then be pushed back towards ground zero. This is called negative dynamic overpressure and can exert massive damage itself, particularly on structures and objects already weakened by the static overpressure and the positive dynamic flow.