A pound-force per square inch (or psi) was a measurement unit of pressure.
At 1 psi a force of 1 pound-force is applied to an area of 1 square inch.
The normal Earth atmospheric pressure is 14.7 psi, which means that a column of air one square inch in area rising from the Earth's surface (at sea level) to space weighs 14.7 pounds.
After the USS Constellation was attacked by the planet killer, the atmospheric pressure on the ship was measured at 11 pounds per square inch. (TOS: "The Doomsday Machine")
The Class F shuttlecraft Galileo had 15 pounds psi of fuel left when it lifted off from Taurus II, which was just enough to make one orbit. (TOS: "The Galileo Seven")