Pressure is simply the total force exerted on a given area. In the SI measurement system, its units are pascals (Pa), and in the imperial system, the units are pounds per square inch (psi). 1 Pa = 1.45 × 10-4 psi. When measuring pressure on the surface of the Earth, it's usually important to take the pressure of the atmosphere into account, so scientists have a unit that does just that. The unit is PSIG, which is known as the gauge pressure. Scientists also have a unit that measures pressure relative to a vacuum. This is absolute pressure, or PSIA. The absolute pressure of the atmosphere at sea level is about 14.7 PSIA where the gauge pressure is defined to be 0. Consequently, you convert back and forth between these quantities by adding or subtracting 14.7.
TL;DR (Too Long; Didn't Read)
The units for gauge pressure are PSIG, and those for absolute pressure are PSIA. You convert between them by adding or subtracting 14.7 psi, which is atmospheric pressure.
Gauge and Absolute Pressure
The standard way to measure atmospheric pressure is to fill a tray with mercury, then invert a graduated tube closed at one end and filled with mercury into the tray. You might have to place a metal plate over the tube opening until it is completely submerged to prevent any of the mercury from falling out. The level of the mercury will fall to a certain level in the tube, but not all the way, because the atmosphere is pressing on the mercury in the tray. The level of mercury in the tube is therefore a measure of atmospheric pressure. At sea level, the height of the mercury is 760 millimeters, which corresponds to 14.7 psi, because 1 mm Hg = 0.01934 psi.
Everything on the surface of the Earth is subject to atmospheric pressure, so any pressure reading you take must account for it. To avoid having to include it in every calculation, scientists define gauge pressure, which, by definition, is equal to 0 psi at sea level. This definition makes clear the relationship between absolute and gauge pressure. Gauge pressure is the recorded pressure minus atmospheric pressure. This is why
1 PSIG = 1 PSIA - 14.7 psi
1 PSIA = 1 PSIG + 14.7 psi.
Which Units Should I Use?
The readings you take on a pressure gauge are always measured in PSIG. That's because, when the gauge is zeroed, it's still measuring atmospheric pressure. If you want to get the absolute pressure inside an evacuated tube, for example, you have to add 14.7 psi to the gauge reading. You might want to do this if you're trying to simulate conditions in space. For most terrestrial readings, however, PSIG is essentially equivalent to PSI, because everything on earth is subject to the same atmospheric pressure.
Gauge Pressure Is Dependent on Altitude
If you center a pressure gauge at sea level and take it to the top of a 10,000-foot mountain, the gauge will show a negative reading. That's because atmospheric pressure decreases with altitude. The difference may be too small to be noticeable in something like a tire pressure gauge, but if you're conducting sensitive pressure studies in a laboratory setting, you should center your pressure gauge at the same altitude as the one in which you are taking pressure readings.