Barometric pressure is simply a measure of the weight of air, as it presses down on the earth's surface.
This may not make sense, at first, because of the general perception we have of air. For example, we use the phrase lighter than air to describe what it feels like to be free of burdens. This also promotes the idea that air is a whispery substance without any weight of its own. In reality, the air we breathe and move through actually has plenty of weight---and potential force. You get a sense of this when you consider the way a strong thunderstorm can knock over a tree, or how a tornado or hurricane can do even worse. In each of these examples, it's the force and weight of the air in motion that's doing the damage; the same way a football player knocks down another football player using his force and weight. Of course, it takes great numbers of air molecules set in motion to unleash this sort of power. But air molecules have this potential, despite the ease with which we can normally pass through them.