To really understand what a shadow is, we really have to know what a shadow is not. When we look around, we see objects because light is bouncing off of them and that light is hitting our eyes. When something blocks the light that would shine on an object, there is a shadow. This is because a certain area has no light hitting it, and so no light can be scattered off of it for us to see.
Matter is usually defined as something that has mass and takes up space. So a shadow is not matter, since it has no mass and takes up no space. Instead, a shadow is a lack of light on a certain area.
I hope this answers your question.
Here's another way to look at it. I'm not sure what gets called "matter" and what doesn't, but I am sure that if it can travel faster than the speed of light it shouldn't get called "matter". Take a little light bulb and very quickly pass your finger above it. On a screen far enough away, the shadow pattern moves faster than the speed of light. /mw
(republished on 07/29/06)