Understanding how pulsus paradoxus happens and why it’s significant requires an understanding of how pressure in the chest cavity affects both breathing and circulation. The chest cavity (thorax) is a closed container that can expand and contract with the help of muscles in the chest wall, back, and floor of the chest cavity (diaphragm).
The lungs, airways, heart, and the largest blood vessels (often called the great vessels) share space inside the thorax. When the chest is expanded by muscles separating the ribs and by the diaphragm dropping down toward the abdomen, the pressure inside the chest falls. This causes air to rush into the airways because the atmosphere around the body now has a higher pressure than inside the chest and inside the lungs.

This is the normal way that humans take a breath. It’s called negative pressure ventilation and it can be compared to the bulb of a turkey baster. When you let go of the baster, the bulb expands and air rushes in.
The whole thing works in reverse as well. If you contract the chest wall and raise the diaphragm, the pressure inside the thorax becomes higher than the surrounding atmosphere and air is blown out. That works with the turkey baster as well. It’s as if you were to take the little rubber bulb from the turkey baster and put it on a bicycle horn to honk it.