Inside a barometer is a sealed can, containing air. This makes it a bit like a metal balloon in that air is trapped, and can neither flow in or out of the can.
If the air pressure outside of the can changes, it'll squash the can slightly. If the air pressure drops, the can will expand. It's these changes in shape that drive the needle on a barometer.
Further details:
All you need to know is that the hydro-static pressure (fluid at rest) acting on a point can be determined by the surface pressure(atmospheric pressure) + (density of fluid)(gravitational constant)(depth). And also that all points at the same depth are have equal pressures acting on them.
So for a simple mercury barometer, A test tube is filled to the top and turned over into a beaker with the same fluid. Atmospheric pressure (Patm) pushes on the fluid in the beaker and gravity pulls down on the fluid in the test tube. So the test tube fluid falls due to gravity, but is pushed back up by the atmospheric pressure. The two forces cancel out and and the system is hydro-static equilibrium. Rmr that all points at the same depth have equal pressures, so the surface of the fluid in the beaker is Patm while the fluid in the test tube at the same level has a pressure equal to (density)(gravity)(depth).
Patm = (density)(gravity)(depth)
density and gravity are constant, so as Patm changes the depth of the fluid in the test tube changes and we can calculate atmospheric pressure by simply measuring the height(same as depth) of the water column.
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