Another key point. The intake system we're looking at has no idea what is taking place on the other side of that intake valve in the combustion chamber. It doesn't matter if there's "fire in the hole," or if the prop is windmilling in the breeze or the airplane is diving with the fuel shut off, engine not even running.
If that engine is turning for any reason, the pistons are hopping up and down, and every time one goes down with the intake valve open, it's sucking more air in. If the throttle plate is closed, it's sucking against resistance, creating suction that shows up as low MP; if the throttle is open, it's not blocking the airflow so manifold pressure remains equal to outside ambient (or perhaps an inch less due to unavoidable restrictions in the induction system).
The rule: Manifold pressure depends on ambient pressure, the position of the throttle plate, and the speed at which the pistons are moving up and down. Manifold pressure does not indicate "power," unless other things are taken into account.
For a silly-but-true example, take an engine that is not running, and lift it from sea level to 18,000 feet. If the MP is 29 inches at sea level, it will be about 14.5 inches at 18,000. The change in MP is entirely due to the reduction in ambient pressure at altitude. Did the engine's power output change when the MP went from 29 inches to 14.5 inches? No, of course not — it's zero either way.
Now a real-world example: Assume you're cruising at some low altitude (say 4,000 feet), throttled well back to about 20 inches MP and 2,000 RPM. (Remember, this means the throttle plate is somewhat cocked, restricting induction airflow.) Now reduce the RPM to 1,200 without changing anything else, and you'll see the MP rise sharply. Why? Simple: The ambient pressure hasn't changed; the throttle plate hasn't changed; the only thing that has changed is the speed at which the pistons are pumping the air. Since they are moving much more slowly at the lower RPM, they are not sucking nearly as hard — not creating as much of a vacuum — so the MP goes up, towards ambient pressure. The natural extension of this experiment is to reduce the RPM to zero, when the MP will rise all the way to outside ambient pressure (about 25 inches at 4,000 feet).
In this example, the RPM has been lowered. The pistons are sucking far less air, the speed of the air going through the intake is less and fuel flow is less. This means there is less power being developed, in spite of a much higher MP! You will also see the airspeed drop off sharply, confirmation of "less power."
Conversely, start once again with our example of cruising at 4,000 feet, 20 inches MP and 2,000 RPM. Now run the RPM up to 2,700, leaving everything else unchanged. Now the pistons are pumping much faster, drawing more air in past the (partially open) throttle plate. That creates more suction — a lower pressure in the induction system — which will show as a lower MP. There will be more fuel flow, and you'll be producing more power at lower MP. (This is complicated by prop efficiency, so give me a little room here.)
To sum up manifold pressure increases in the runup when rpm is decreased because the pistons aren't moving up and down as fast thereby creating less suction against the partially closed throttle plate.
Manifold pressure should increase when you check the magnetos for the same above reason- less power being produced due to a less efficient burn of the fuel air mixture.
Manifold pressure initially on the takoff roll will be about an inch below ambient pressure due to imperfections within the intake and filter which somewhate starve the engine. Once you get some speed ram air effect in most airplanes will cause the manifold pressure to increase somewhat. This is also why you should carefully check the manifold pressure gauge during preflight- notice there is no green arc on a manifold pressure gauge indicating what normal takeoff pressure should be( at least in non-turbo engines). Takeoff manifold pressure will vary with ambient atmospheric pressure- read elevation for all practical purposes.
Knowing all this its alaways fun to question you're student when you are flying a twin and ask them "so why does the feathered engine sill registering some manifold pressure?"