What does the trimpot on my Switching Power Supply do?
No doubt it's just a final tuning potentiometer. Even on the pictures you linked it's described as V adj which stands for voltage adjustment.
It's a way to tune your power supply's output as it can vary depending on temperature/humidity/wall-plug voltage/etc.

It's usually set properly and doesn't need to be touched. But you can connect a multimeter to check if your power supply gives the voltage you need. 

If you are not familiar with the subject but still want to do it yourself, it's good to set your multimeter to the highest available range and make sure that AC/DC is properly chosen.  Now you can measure voltage. You can set the range closer to the expected values then. Usually multimeters have a range around 20 or 30V DC which is propbably what you expect from your power supply. In such a range you should see something like 12.000. If it varies from 12.000 you can then precisely adjust it to get as close as possible to this value. But watch out... cheap power supplies can cheat you. When the are have a load on the output (your 3D printer for example) they can reduce voltage.