How exactly does atmospheric pressure work?

You know what's above your head right now? Air, tons of air actually. Atmospheric pressure is just the weight of that entire column of air pressing down on everything below it - you, the ground, objects, everything. The higher you go in altitude, the less air there is above you, so the pressure drops. That's why it's harder to breathe in the mountains or on a plane - you've got less air weighing down on you.

Air molecules are constantly moving and they hit everything they encounter - your skin, a table, a barometer - billions of times per second! This microscopic bombardment is what creates that force we call pressure. That's why when you change altitude, you feel the difference: there are fewer molecules doing that work, so fewer impacts, so less pressure.

What people often forget is that pressure acts in all directions at the same time, not just downward. When I set up my aquarium, I realized that water pushes with the same force on the side walls as it does on the bottom, and it's exactly the same with air - it crushes us from everywhere but we feel nothing because there's an equivalent pressure inside our body that balances it out.

The earlier answers explain the concept well, but they miss that it's all about balance. That's why we can breathe normally even with tons of air weighing down on us - as long as the pressure inside and outside are balanced, you feel zero crushing sensation.

Don't think it's just pushing down from above, or you'd figure you should get crushed like a pancake. In reality, when I pump up my bike tires, I can definitely feel the air pressure inside pushing in all directions at once - on the valve, on the tire wall, everywhere. It's the same with the atmosphere around you, it pushes you from everywhere uniformly so you don't notice anything. The guys talking about the weight of the air above are right, but it also acts horizontally and upward with the same intensity.