The eyes are measuring the number of photons of each color that are hitting a given point of the retina – that are coming from some direction.
This is a function of time, $f(t)$, for each point. However, when this function is changing too quickly, the eye can't see the changes. Effectively, the eye may also see the average of $f(t)$ in each period of time which is as short as 1/50 second or so. That's why 24 or 25 or 30 or 50 frames per second are usually enough for a TV screen.
If the fan frequency is at least 1 blade per 1/50 second, which is the same as 10 rotations per second for a 5-blade fan, for example, the following is true:
During 1/50 seconds, each point of the image where fan blade may either be or not be sees a full period, so the perception is no different from the perception in which the color is averaged over those 1/50 seconds. But the averaged color of each point is pretty much the same. It's a weighted average of the (RGB) color of the objects behind the fan at the given point; and the color of the fan blade. The weights in the weighted average are determined by the thickness of the fan blades (relatively to the circumference), and these weights may actually depend on the radial coordinate $r$.
So what we see is not "quite" transparent – the contrast is lower – but it's enough to see what's behind; the color of the things behind the fan is mixed with the color of the blades; and this mixing occurs pretty much independently of the location relatively to the axis of the fan (if the fan blades' color is uniform), and independently of time (because of the averaging over the 1/50 second time intervals).
Note that the 1/50 second resolution depends on the neurology – abilities of the eye, nerves, brain etc. However, even if the brain were perfect, there would exist certain limitations that couldn't be beaten. The number of photons coming to each retina cells per second is finite and the inverse of this number basically determines the best possible time resolution one can have for the given "pixel".