Principle of the mercury barometer
(pps 27 & 28 in the ClassNotes for a little longer version)

Air pressure at any level in the atmosphere depends on the weight of the air overhead.  A mercury barometer is basically just a scale that measures the weight of the atmosphere above.

Easily the most impressive seesaw (teeter totter) that I've ever seen (source of this image).  If you understand how this works you'll be able to figure out how mercury barometers function.	A barometer is essentially a balance. The weight of the atmosphere is balanced by the weight of a much shorter mercury column.

You can't use an ordinary pan balance to weight the atmosphere (because air is pushing down on both sides).  A U-shaped tube filled with some kind of liquid that can slosh back and forth would work.  Such an instrument is called a manometer and is often filled with mercury.

To turn the manometer into a true barometer, we'll extend the tube on the right and close the top so that air isn't pushing down on the mercury.  We'll also use somewhat larger cylindrical columns of air and mercury that completely fill the insides of the tube.

The weight of a very tall cylindrical column of air is balanced by a much shorter cylindrical column of mercury.  The height of the mercury column will change as air pressure varies.

Mercury is a liquid.  You need a liquid that can slosh back and forth in response to changes in air pressure.  Mercury is also very dense which means the barometer won't need to be as tall as if you used something like water.  A water barometer would need to be over 30 feet tall.  With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier).  Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube (there's some gas, it doesn't produce much pressure, but it would be hazardous you if you were to start to breath it).