That means inflate them to the pressure stamped on the tire sidewall. However the assumption is that you are running stock tires or at least the same load range as original. If you are running a higher load range (i.e. higher psi), it is not a good idea to inflate the tires to that higher psi. That will make the tires too stiff for the light weight they are carrying and you will beat the trailer to death.
If you look at a load inflation chart for say Maxis, you will see that at the same psi, a load range E tire will carry the same weight as a load range D tire. Meaning if both are inflated to 65 psi, then they have the same load carrying capability at that psi. But the E tire can be safely inflated to 80 psi while the D tire cannot. On the other hand, the E tire has more mass and will run slightly hotter than the D tire at an identical psi, which is not a good thing. In short, if your trailer came stock with 65 psi tires and you now have 80 psi tires, I would run them around 70 psi as a compromise between running too stiff and running too hot.
Or you can weigh the trailer and use actual weight and the load inflation chart to set the tire pressure. Even then, I would run about 5 psi above the stated pressure for additional margin against minor changes in loading from cargo, side winds, road crown, etc.
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