A shadow is simply the region behind an object where light is not due to blocking by an opaque object. It might be easier to think of light as photons, and the shadow as the space which photons from the light source cannot reach due to the occluding object. Although a shadow is often thought of as a 2D area, that is only a reverse projection onto a surface; an object's shadow is actually the entire volume where light is blocked. There are different types of shadows though, called the umbra and penumbra. The former is the region which has no light at all, and the latter is the region which can be reached by some light, but less than an unobstructed region.

The sizes of these regions depends on the size of the light source and the distance from the object.

I'd say a shadow is the pattern of something that blocks light. So the light is bright where it's not blocked by the object, and the light is dim where it's blocked by the object, and we call that dim pattern the shadow.

Light cannot pass through opaque objects. Anything that is in the shadow of one means that it is not illuminated, since the light is reflected or absorbed before it can get to the shadow.

A shadow requires a source of light and an object. The shadow is formed by the object blocking the light, and the shadow will always be in an area farthest away from the light, and of course, the shadow will often be darker than the area around it and marked by a boundary.

If there are more than one source of light, there will be more than one shadow. If there is light from every direction, like surgical lamps are designed to give, there would be no shadow. If there is no light, there is no shadow, strictly speaking. Shadows can be multicolored or three-dimensional as well, and those are fascinating from a both physical science perspective and an artistic perspective.