To keep it simple at first, think about this: what can we learn about the
shape of something just by looking at shadows? Let's shine spotlights on some
different shapes and look at the shadows they make:
I can't tell a whole lot, except for how wide the shape is in the direction
the light is shining on it.
That's a start. Try this:
Oh, I get it. Each direction we look at the shadow tells us something more.
Does that mean that the more ways we look at it, the more we know about it?
Exactly. That's why real CAT scan machines go around in a circle: so they can
take x-rays from all sides.
Um...wouldn't it be easier to just spin the shape and watch the shadow change?
It would give us identical results. Of course, the most we could ever learn
using plain old visible light is what the outside contours of something are.
But x-rays enable us to do a similar trick on the inside.