Air Pressure
Air pressure is the force exerted by the weight of the atmosphere on a surface, averaging about 101.3 kilopascals at sea level and decreasing with altitude.
Definition
Air pressure is the push exerted by the weight of the atmosphere pressing down on everything below it, averaging $1{,}013.25$ millibars at sea level and decreasing with altitude because there is less air overhead, measured with a barometer and following the hydrostatic relation $\frac{dP}{dz} = -\rho g$, which combined with the ideal gas law gives an exponential decrease with a scale height of about $8\ \text{km}$. Warm, less dense air creates low pressure while cool, dense air creates high pressure, and air flows from high to low pressure to produce wind; in the free atmosphere, the pressure gradient force balances the Coriolis force to produce geostrophic wind flowing parallel to isobars, and even the small percentage differences between typical highs and lows are enough to drive all large-scale weather.
Example
Ears pop when driving up a mountain or taking off in a plane because outside pressure is dropping and pressure inside the ear has to catch up, and Mount Mitchell at $2{,}037$ meters has about $20\%$ lower pressure than sea level, low enough that water boils at about $93^\circ C$ instead of $100^\circ C$. Hurricane Florence had a central pressure near $937$ millibars at peak intensity, while the lowest sea-level pressure ever recorded was $870$ hPa in Typhoon Tip in 1979 and the highest about $1{,}084$ hPa in a Siberian winter anticyclone.
Key Insight
At sea level, air presses on the body with about one kilogram of force per square centimeter, but it goes unnoticed because air inside the body pushes back with equal force, and on a weather map an area of low pressure usually means rising air, which cools and forms clouds, which is why an "L" on the map usually points to rain. A column of warm air is taller than a column of cold air at the same surface pressure, so at any given height the warm column has higher pressure aloft, and that aloft gradient is what starts the great circulation of air from the tropics to the poles.