When we discuss weather systems in forecasts you may hear mentions of pressure associated with these changes. Pressure concerning weather has several different names, known as simply "air pressure" and also "barometric pressure." This all describes the same force pushing down on us every day from the weight of the atmosphere above. The pressure of the air up above is a big piece of how weather works and why the environment behaves how it does.
Pressure isn't equal across the planet; if it was, air wouldn't be able to move and conditions would never change. But Earth is uneven and varies between land and water in chaotic patterns, leading to differences in pressure overhead. For one example, there's less air over a mountain than at lower elevations, leading to less force (pressure) at the peak. This difference in pressure forces air to move to try and stabilize the atmosphere, which generates wind.
Winds carry moisture, heat, and other ingredients that lead to storm development. This wind is all due to air pressure that underlies all weather systems. Aside from these weather impacts, pressure changes can also have direct impacts on our bodies. If you feel aches, headaches or joint pains when storms are moving through, this could all be due somewhat to changing pressure. As the air changes around us it constricts and stretches our bodies to an almost unnoticeable degree, but enough to keep us feeling under the weather.