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The planes landing at Sydney Airport have what looks to be sheets of steam pouring off the wings. Larger planes have multiple contrails while smaller regional planes only have these sheets.
This is the first sunny day after a large storm. There are patches of dark cloud.
From the link posted by fooot, I've learned that it's condensation, but what is the mechanism by which it forms? The video shows planes in poor weather, but visibility here is excellent, with 20% cloud coverage.
We know that the pressure decreases over the wing. We can also assume that a particle of air travelling above a wing does it so fast that does not have the time to exchange energy with the sorrounding ones (called adiabatic process)
We can now look at a pressure/volume diagram for an adiabatic process that goes from "high" pressure (the free undisturbed air in front of the aircraft) to low pressure (the air on top of the wing):
image source (currently unreachable)
As you see from the diagram, if you move along the Adiabat line from the top to the bottom, the temperature drops. If the air has already a temperature near the water condensation one and a high enough humidity, it will condense. From the Wikipedia article linked before:
Adiabatic cooling occurs when the pressure on an adiabatically isolated system is decreased, allowing it to expand, thus causing it to do work on its surroundings. When the pressure applied on a parcel of air is reduced, the air in the parcel is allowed to expand; as the volume increases, the temperature falls as internal energy decreases.
Isotherm (meaning "same temperature") are 2 lines where, moving along them, the gas does not change temperature. The Th (Temperature high) has higher temperature than the Tl (Temperature low), as pointed out from the Th>Tl remark. Moving from one red line to the other you change temperature.
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An important concept here is dew point. The dew point temperature is related to the current temperature and the humidity of the air. For example, near sea level, a temperature of 51°F and humidity of 86% gives a dew point of 47°F. If air is cooled below the dew point, the water in the air will condense. You can see this effect on a cold glass; the air near the glass is cooled below the dew point, so the water in the air condenses onto the glass.
When humidity is high, the dew point is very close to the air temperature, which is why it's easier to get condensation when the humidity is high. When the air temperature cools down to meet the dew point, fog forms. The water vapor in the air is condensing, but without a surface to gather on, it condenses into small droplets that form fog. Humidity will be high in foggy conditions, and often when it is raining, but can also be high in other circumstances. Jan Hudec's comment notes that as water is evaporating from the wet ground, there can also be high humidity.
Federico's answer does a good job of including the gas physics at work on the airplane wing. The important link is that as the wings create a low-pressure area, the temperature falls along with the pressure. If the dew point is high enough, this temperature drop may only need to be a few degrees. The water vapor condenses in the air, with the effect that you noticed. Once the air has passed over the wing, the pressure eventually returns to normal, along with the temperature, causing the water to evaporate again.
The small "contrails" that form are from a similar effect. At locations such as the edges of flaps, a vortex is formed. This is a section of tightly spinning air. Similar to the wings, the acceleration of the air lowers its temperature and pressure, causing the condensation to form in the air. The vortex will eventually dissipate, and the condensation evaporates.
Actual contrails that form behind planes at high altitudes are due to a similar but different effect, and there are some questions here discussing them.
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.
