A manometer uses a liquid to measure differences in pressure. For heating purposes it measures the difference between the inside of the flue pipe and the ambient pressure outside the flue pipe. A more common term used for what it is measuring is "draft". It can be important to understand what this is especially if you having issues with your coal burning appliance. If you have too much draft you will be using a lot of coal and expelling a lot of heat out of the chimney. Too little draft and you will have difficulties keeping a fire lit.
The manometer's components consist of the indicator box with the reading, a fitting installed on the flue pipe and tubing connecting the fitting to the the indicator box. The fitting for the manometer tube installed on the flue pipe is placed after the exhaust port of the heating appliance and before a barometric damper if present. A tube is installed between this fitting and the manometer device. The tube connected to the flue pipe fitting must be able to handle the temperatures present at this location, a short piece of copper tubing is commonly used. The reading can also be taken at the firebox by having a fitting installed through the wall of the of the heating appliance. Some appliances may already have a threaded port that the fitting can be threaded into, when not in use there is a threaded plug that seals the port.
Once you have a reading it can be used to calibrate / set the counter balance weight on a barometric damper. The draft measurement scale is usually in inches of water. Different heating appliances recommend different ranges but generally they are around .05" H2O