When performing a magneto check or exercising the propeller prior to take off (constant speed propeller), you notice that as the rpm drops the manifold pressure rises slightly. Why does the manifold pressure rise?
On the intake side, the engine is effectively a vacuum pump; it's sucking in air past a restriction in a duct - the venturi and throttle plate, creating a partial vacuum in the intake passage, and measured as total pressure in inches of mercury (In cars, the MP gauge is labelled "vacuum"; similar, but expressed as a differential between ambient and duct pressure instead. The problem with car style vacuum gauges is you can't use it to measure horsepower because you don't know the absolute pressure in the intake duct, only the differential, and you'd have to know the actual ambient pressure to work out what is the actual intake duct pressure).
With the restriction being fixed (not moving the throttle), anything that changes the pumping rate (directly tied to piston speed, therefore RPM) affects the amount of suction created between throttle plate and cylinder. Decrease the pumping rate (or sucking rate you might say), and the vacuum goes down/MP goes up. And vice versa.
So anything that raises RPM without moving the throttle plate moves MP down a bit because the piston is sucking harder because it's going faster, and anything the reduces RPM without moving the throttle plate moves MP up a bit, because the piston's moving slower. As you get familiar with this, you learn to drop MP about half an inch below target when following up with an RPM reduction, knowing it will come up as you reduce RPM. And vice versa on power increases.
Think of manifold pressure as being the pressure of the air between the throttle door and the intake valve to the engine cylinder.
Consider that the engine is pulling air through this area. If you impede that flow by closing the throttle, the pressure decreases. Why? The engine is still pulling the air very strongly like a vacuum pump, but the throttle door closing, blocks the flow, so it creates a drop in pressure. If you open the throttle, it gets out of the way of the airflow and therefore there is a pressure increase because the air is being replaced more quickly/easily as it is being drawn into the engine cylinder.
So, if the engine is creating suction and thus dropping the pressure, then it follows that decreasing engine power via methods other than changes in the throttle setting, would cause an increase in manifold pressure because now, rather than changing the impedance of the airflow vs. the suction of the engine, the amount of suction generated by the engine is what is being reduced. Reducing the amount of vacuum pressure (suction), leads to an increase in air pressure between the throttle door and the intake valve at any given throttle position.