I admit it isn't obvious. But it's about transportation of oxygen from the limited supply at the surface of the water to the places its being used. The more the water flows around the tank, the more oxygen is available.
If there's no flow at all, oxygen goes into the water at the surface (diffusion) and then slowly spreads down the tank (more diffusion) and then gets absorbed by the bacteria in the gravel or filter. When you add a water pump, oxygen-rich water is physically carried to the bottom of the tank, and oxygen-poor water is carried to the top. This means you remove the slow diffusion bit in the middle, speeding the whole process up. The bacteria in the filter or gravel get more oxygen per second, so can multiply up to a larger population. The more water flow, the more oxygen is being moved about, and the more the bacteria can multiply.
The diffusion rate at the top of the tank is basically dependent on the concentration of oxygen on either side of the air/water boundary. When the water is still, the oxygen concentration in the surface layer will be relatively high because nothing is using it up and it can easily accept oxygen from the air. In other words, the diffusion gradient is gentle, and the net intake of oxygen will be low. A water pump moves oxygen-poor water to the surface instead. There is a steep diffusion gradient now, because the deoxygenated water has little oxygen while the air has lots. So the rate of diffusion will be faster. The more the pump moves oxygenated water away from the surface and deoxygenated upwards to the surface, the steeper this gradient will be, and the faster the oxygen uptake gets.
It's essentially the same thing as happens in your lungs. Oxygen isn't left to diffuse into the blood from the air and then diffuse around the body. That would be too slow. Instead deoxygenated is pumped to the lungs so that it rapidly accepts oxygen, and oxygenated is pumped away to the rest of your body so that it can supply your tissues. Think of the surface of the water in your tank as the lungs, the pump as the heart, and the water as the blood. It all makes sense now! The faster the pump, the better the circulation of oxygen.
Of course there are limits. Even if you have a super-filter that turned the water over 20 times per hour, filtration would level off at some point because other factors, like ammonia concentration, would become limiting.
Cheers, Neale
I can't see that fast flow rate actually benefits bacterial growth within filters.