Federico's answer nails exactly what's going on, although for us Poetry majors, the graph can look confusing. Let me add this simplified explanation, plus address something that showed up briefly in a now-deleted answer.
In short, condensation happens with cooling. We see liquid condense on the side of a cold glass of liquid on a hot day, and happens when air "here" (near the glass) is cooled below the dewpoint, so the humidity condenses into water drops on the glass.
When you see clouds/condensation/vapor trails forming above or directly behind the wing of an aircraft landing in humid conditions, the same basic phenomenon is taking place, but instead of condensing ONTO a surface, the condensation takes the form of a "cloud" or "vapor trail" streaming behind the wing. Here, the cooling is caused by the air: with the air above the wing having lower pressure, it has cooled (PV=NRT, vaguely remembered from physics, Pressure goes down, so does Temperature), and when the air is humid enough with the spread between temperature and dewpoint very close, that cooling is enough to give you the condensation.
A similar but distinct phenomena that causes condensation ON the wings, but not BEHIND them, is cold-soaked fuel. When an aircraft has been flying at high altitude for a long time, where the temperatures are far below freezing (-40 degrees or so), the fuel inside the tanks in the wing gets cooled to similar temperatures. On the ground, this fuel acts like the liquid in the glass, and you get condensation on the wings, and frequently, "cold soaked fuel frost" that forms after the condensation freezes onto the surface of the wing.
This is NOT what causes the vapor trails observed in the original question, because there isn't enough time for the rushing air to be cooled by the cold wing. THAT happens due to the change in air pressure. Parked, you don't have the lift/low pressure, so that cooling mechanism is gone, but with stationary air, you have the other effect at work.