Planted Tank covers the issue very well in post #2: Think about what happens in the water (fish and plants, giving and taking Co2 and O2) and compare it to the equilibrium with the air.
Remember though, that water that is not moving will not get enriched with either CO2 or oxygen. These gases enter the water at the surface, then diffuse very slowly through the rest of the volume. Only the top inch or less is really in equilibrium with the air. The rest of the water is in some sort of balance based on the fish and plant loads, and varying with their changing needs.
There are other reasons why more surface motion might be desirable in the tank.
Reduces surface scum. The gases won't equalize if they are not in contact with the water. A film of lipids or proteins on the surface seals it off. breaking up that scum and circulating it to get it trapped in the filter and removed is a very important reason to maintain some surface movement.
Daytime: Circulates that thin layer that is enriched with CO2, and mixes it with the CO2 depleted water below.
Nighttime: Circulates that thin layer that is enriched with O2, and mixes it with the O2 depleted water below.
Without water movement only the very top layer will really be gaining or losing gas to the air.
Equalizes the temperature. Especially important if the tank is too hot, this allows the fastest moving molecules to escape, thus cooling the tank.
Keeps the fertilizer and other minerals the plants need circulating, so as the area next to the plant gets depleted more moves in. (This is not so much surface movement, as movement in general)
And in extreme cases... kills duck weed
Overall the optimum balance between CO2 loss (good for fish, bad for plants), O2 gain (good for fish, good for plants (they use oxygen, too), and very important for microorganisms, and other benefits of moving water has usually been found when there is a gentle ripple at the surface. No bubbling, no splashing.
A filter, power head, or even bubbler that lifts the water from the bottom and sheets it gently across the surface does the best job at creating that gentle ripple. I do not much like bubblers, though. To be effective at moving enough water they do splash more at the surface.