What the atmosphere is
The atmosphere extends hundreds of kilometres upwards from the surface of the earth. It is the air-filled space surrounding our planet.
A column of water, a column of air — the same argument
At any point inside the water in a filled vessel, a pressure arises because of the water above that point.
In the same way, at any point inside the atmosphere a pressure arises because of the weight of the air above it.
Atmospheric pressure
The pressure arising at a point because of the weight of the air above it is called atmospheric pressure.
Why we are not aware of it
We live at the bottom of this atmosphere, so atmospheric pressure acts on us at every moment. We do not feel it because that pressure is applied equally in every direction — and the pressure inside our bodies matches it.
Instead of measuring the column of air
The atmosphere is hundreds of kilometres tall and the air thins out as you go up, so P = hρg cannot be applied to it directly. Instead, that pressure can be measured by balancing it against a column of liquid.
The first to measure it that way was the Italian scientist Torricelli. His apparatus is on the next page.