Doremus has the best explanation so far.

Personally, I view the optical system as two cones, meeting at a point in the middle of the lens/shutter unit, and extending out in both directions from that point at the angle of view of the lens. The "rear" cone projects the image circle onto the film plane, at a very reduced size. This also means that the cone between the lens and the subject (front) is much, much larger, than the cone between the lens and the film plane (rear).

If the lens were exactly halfway between the subject and the film plane, then moving the lens would have the same result as raising the camera's position.

Since the lens is much closer to the film plane as a rule (when not doing closeup work) a small shift of the lens position will produce a large shift in the image projected onto the film plane.

Similarly, it doesn't require much tilt to produce a substantial shift in the plane of sharp focus.