Pressure is exerted in all directions: compressed air pushes equally in all directions. Inside of an air tank, for example, if the air pressure reading on the gauge is 100 PSI, on every square inch of surface inside that tank, the bottom - the top - and on the sides, the compressed air is pushing out with a force of 100 PSI.
If the load that you are trying to lift is 100 lbs., and the surface area of your piston inside your actuator was 1 sq/in in size, then your compressed air supply pressure would need to be at 100 Pounds Per Square Inch to give you the force you would need to move the load.
This is a bit theoretical, as compressed air force is also consumed by friction caused within 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 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.
Having a safety margin in actuator size means that, if the supply PSI pressure to the cylinder should be reduced for any reason, perhaps by consumption of compressed air elsewhere in the same lines, the actuator will still have enough force to lift the load.
PSI is a measure of force available in an air circuit. Reocgnizing what it means and how it applies will help the design of air circuits be more effective.