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psi stands for pounds per square-inch.
It is a measure of pressure, and is the equivalent pressure of putting one pound on a square-inch of area.
For example, someone weighing 180 pounds standing on his feet, with a footprint area of 72 square-inches would exert a pressure of 180 pounds/72 square inches = 2.5 pounds per square-inch, or 2.5 psi.