PSI, or pounds per square inch, this is the measure of pressure on an area, and it is a measure of force.
Pressure is the amount of force exerted in a specific unit of area; in the case of compressed air, force applied onto a single square inch of surface.
If the load that you are trying to lift is 100 lbs., and the surface area of your piston inside your actuator is 1 sq/in in size, then your compressed air pressure would need to be at 100 Pounds Per Square Inch to give you the theoretical lift force you would need for the application.
I say theoretical, as compressed air force is also consumed by friction caused within the actuator itself (seals against rod and piston) and friction caused by whatever the rod-end load may be sliding on or against. All of this friction adds to a greater-than-theoretical actual force requirement for your real world application.
If you needed 100 lbs. of lift, and you expected that your air supply would be at a constant 100 PSI., rather than having a 1 sq/in sized piston inside the cylinder, you might consider using one with a 2 sq/in piston. By moving up in actuator size, you have allowed for significant additional force to be available to handle the increased load due to friction.
Also, if your available air pressure should be reduced by consumption of compressed air elsewhere in your plant, building in over capacity in a cylinder application means that you might still have enough air pressure left at that location to lift your load, even if the supply of compressed air was diminished by other uses.
PSI is a measure of force available. Simple as that.