Barometric pressure is a routinely measured aspect of the atmosphere with a critical role in weather forecasting. Essentially, air pressure is proportional to the weight of the air above a point. Although the air pressure reading at any single point has little bearing on the weather, air pressure patterns (higher and lower) across a region indicate areas of sinking or rising air, which is directly related to weather. Downward-moving air generates clear weather whereas rising air makes clouds and precipitation.
To be able to forecast how these patterns of pressure will change over time is critical to weather forecasting. This is why a falling pressure or a rising pressure is a telling sign. Differences in pressure across distances force air to move to attempt to equalize these pressures, so differences in air pressure is the primary reason the wind blows.