“Shadow” just means a dark area, but why do we call it “a shadow is ‘on’ the surface,” not “a shadow is a dark surface”?
A shadow is not a surface. It isn't anything tangible at all. A shadow is just the effect of a reduction in light caused by blocking a direct light source.
Consider this: if a surface was red, you'd describe it as "a red surface". If a shadow were to cast over it, the perceived shade of red may change slightly, but you would still say it is a red surface.
Remember that we use "on" as a preposition, not only to indicate contact between two things, but also to show the effect of something on something else. A shadow is not actually in contact with anything, it is just an effect on our perception of light and colour. So, referring back to my example, you might say that the red surface has a shadow on (or 'over') it.
Because shadow is the figure that's cast upon a surface by blocking the light. In other words, you need the surface to have a shadow. And the "on" preposition is used to specify which surface the shadow is being casted upon, it doesn't necessarily imply physical contact (see 4 here).
If there is no surface to be obscured from the light, or thing to cover the light reaching a surface, there is no shadow.