three visceral cavities
How we can observe exactly what is going on in the inner workings of the body by six little spots on the wrist, is not entirely clear. But the best explanation would be that the pulse is a blood vessel that carries the blood/fluid. It's driven by the heart, so by reading the pulses properly, you can see what the heart is doing. The other organs can also affect the heart. Sometimes, there is an obvious connection — the lungs, for example. Sometimes, the connection is not as obvious — like, the pancreas.
The radial artery also runs along a major meridian. Blood is to artery as Qi ("chee") is to meridian.
The analogy we were given was ripples in a pond when you throw a stone in. If you understand how the waves travel and are affected by objects in the pond, how constructive and destructive wave interference works, you can tell by the ripples that there is a goose and a toy sailboat somewhere in the middle. You might be able to tell their positions and orientations. As well, there is untrimmed grass along the circumference (as opposed to a brick-lined edge) and there's a fallen tree branch laying half-way in the water at one point.
Because the body is a harmony of systems, if one thing is affected, there will be an effect on the rest of the body.
I should try to explain 五臟六腑 (the Five Major Organs and the Six Hollow Organs) sometime soon. It's not entirely the same as in Western Medicine. As concise as I can explain it, Western Medicine sees organs as function based whereas Chinese Medicine sees them as a harmony or balance.