The differential manometer is a U tube manometer. It consists of a U shaped tube. The tube is filled with a liquid, usually water or mercury.
The two limbs of the U tube are connected to two points in a pipeline or any other hydraulic system.
The pressure of the two points act upon the liquid in the differential manometer. The liquid in the two limbs will not be at different levels as the pressure in the two points will be different.
The difference in the levels of the liquids in the two limbs gives the difference in the pressure. The U tube can be calibrated to give readings directly in units of pressure.