What does a barometer measure?

Air pressure, and the first one settled an argument about whether a vacuum could exist at all. Torricelli in 1643 filled a glass tube with mercury, upended it in a dish, and found the column fell to about 76 centimetres and stopped - held up by the weight of the atmosphere pressing on the dish. The empty space above it was the first sustained vacuum anyone had made, in a period when the received wisdom held that nature abhorred one.

Pascal then took a barometer up a mountain, correctly predicting the column would fall as the air above thinned. That established both that the atmosphere has weight and that it has a top, which is not obvious from the ground.

It became the basis of weather forecasting because pressure changes lead the weather rather than describe it. Falling pressure means air rising, cooling and condensing - cloud and rain; rising pressure means air sinking and clearing. Old dial barometers are marked stormy, rain, change, fair and very dry for exactly this reason. The instrument is measuring the mass of the air above you, and the fact that this predicts the weather is one of the tidier coincidences in physics.