A pounds per square inch (or psi) was a measurement unit of pressure, which was equal to the force of 1 pound applied to an area of 1 square inch.
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")
For reference, the normal atmospheric pressure on Earth at sea level is 14.7 psi.
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")