Well from a physical point of view, objects simply scatter the light that hits them, and their color comes from their absorption spectrum.
So the perceived saturation depends on the combination of incoming light and absorption. Say greenish light hits an object that absorbs more green than other wavelengths (which makes it look purple under “white” light), it looks pale because it effectively flattens out the spectrum which we perceive as grey.
If source and absorption have similar shapes, the peaks get pronounced and the color looks more vibrant (see in your local supermarket how they use light to make tomatoes or meat look more appealingly red than they actually are in daylight).
So, physically it’s all a matter of the various light sources (strong direct light, ambient/indirect light). Ambient light tends to “bounce” (get scattered) multiple times before it hits the eye, and as said, depending on the surfaces it hits, this can add or reduce peaks in its spectrum. So when painting, you need to get a feeling for how the scenery around the object affects the light that hits the object you are painting, there is no standard answer to the question if shadows are more or less saturated than highlights.
But there’s also another very important factor: Dynamic range.
Monitors, and even more so photos/prints can only reproduce a very limited range of brightness, our eyes can deal with with much higher contrasts with ease. So a lot of the contrast in images we see on monitors and pictures is actually an illusion, the dynamic range has been compressed significantly.
This inevitably influences the saturation too, very bright parts tend to desaturate even though in reality we would see a very vibrant color just much brighter color, but the medium can’t reproduce this.
Our eyes are very used to this compression, so a lot of the saturation in an painting also has to do with the impression of contrast/brightness it should give.