Answer:
While watching the air pressure change, the change that occur within the barometer is that the barometer (if aneroid barometer) contains within it a partially evacuated (vaccumed) steel corrugated box. The top surface is held by a strong spring to stop it from collapsing.
If the air pressure changes, the surface moves up or down with a decrease or increase in air pressure respectively. This movement is transmitted and amplified by a connected system of jointed lever and chain that passes around a grooved wheel. This transmission is to a pointer that is deflected with these change and movements to give the reading on the scale. The scale is is often calibrated in millibars; higher pressure indicates a bad weather.