When we refer to pressure we usually mean the absolute pressure. This is the pressure exerted with a inverted manometer having the closed end evacuated, below left.
Because the atmosphere exerts a pressure and a vacuum does not, the liquid in the manometer is pushed around the u bend by the atmosphere.
If both ends of the manometer are open, the liquid level is the same on both sides. Suppose now that one end of the u bend is filled with a gas and cloed. If the pressure exerted by the gas is greter than atmospheric pressure, then the gas will push the liquid against the pressure exerted by the atmosphere. The difference between atmospheric pressure and the gas pressure is called the gauge pressure,
here is the pressure exerted by the gas, the sum of the gauge pressure and the atmospheric pressure, so that
In the example shown above the gas pressure was greater than the atmmospheric pressure, so the gauge pressure was positive. If the gas pressure is less than the atmospheric pressure then the gauge pressure is negative sinceThe atmosphere pushes the liquid in the u bend against the gas as shown below.