The tube of the manometer is partially filled with mercury or water which settles in the bottom of the u-shaped tube, before the atmosphere being measured is allowed to enter the open end of the tube and move against the fluid in the tube. The difference in the height of the liquid in the sealed side and open side of the tube is the measure of the pressure of the atmosphere or gas being tested.
When these devices were first put into use, they commonly used mercury to measure instead of water. This practice lead scientists to the use of the term millimeters of mercury or mm Hg. As science developed the terms changed and one mm Hg is now called one Torr. This measurement signifies that one Torr of pressure is exactly one millimeter of change in the liquid inside the tube. The sealed side would go up by one millimeter while the open side of the tube would drop.
The use of these meters isn't exclusively to test air pressure alone. They are also used to calibrate various devices. They can vary from the u-shape that is commonly seen, to versions that are smaller, portable and connected to a computer interface. These types of setups can be connected to pressure sensitive machinery and used to adjust or calibrate the amount of pressure exerted by it.