According to the race tuner manual:

MAP - Manifold Absolute Pressure - This sensor provides input signals to the ECM and reacts to intake manifold pressure and ambient barometric pressure. Intake manifold pressure reflects changes in engine speed and load. Ambient barometric pressure reflects changes in atmospheric pressure caused by weather conditions or changes in altitude. The ECM uses the inputs from this sensor to help calculate how much air is entering the engine. It's located in the intake manifold on top, just behind the throttle body.

What I don't understand is how this reads the speed and load and ambient barametric pressure at the same time. What exactly does it reveal?

speed + load + barometric pressure = manifold absolute pressure...

So it's a pressure figure that's affected by speed, load and barometric pressure which reveals the density of the air when it's checked against the temperature...

Question: So when there's more speed and load it actually sucks in air harder and therefore it's denser given a constant temp and barometric pressure? What makes the engine pull air harder when there's a heavier load?

 

Affected by and calculated from are two differant terms. The cylinders create a vaccum sucking air from the atmosphere through the throttle body and manifold. The single biggest impact is the position of the throttle plate. That impacts the size of the charge being loaded in the cylinders, i.e. the load. Exactly how throttle position relates to map pressure depends upon atmospheric pressure. Engine speed, given a build, determines how pressure in the cylinder relates to pressure in the manifold, i.e. the volumetric efficiency.

Actually measuring it is fairly simple. It's just a diaphram with a sealed referance pressure on one side and the manifold on the other side. How far that diaphram deflects is an indication of the pressure in the manifold relative to the referance pressure.

 

The MAP sensor measures, "ambient barometric pressure" during the startup. Before the engine starts it takes a reading and remembers it for that time it is on. That way it knows altitude and can adjust itself.
If you happened to change altitude a lot in one session it would be a good thing to stop and restart to get a better adjustment.
Where I live, Gulf Coast, I would have to ride for 2-3 days steady to affect that.