It affects the amount of ambient (background) light that has no direction like the light from a star has.
Ambient light comes from every direction, and on default settings it is much too high for a real space. It causes the shadowed (or actually, non-illuminated side as FSO doesn't support shadows) side of objects to "shine out", whereas in the real space it would be almost or completely dark.
So, the default setting is quite high, and lowering it makes the game a bit darker in overall appearance, makes shadows sharper and other nice stuff like that. As I said, I like it when I almost can't even see the dark sides of the ships. -ambient_factor 65 is good for this, I've found. Most seem to keep it a little brighter in, say, 75 or so.