How does a dirty or bad mass air flow sensor make the engine run?

 

It will usually cause bucking, engine can ping/knock, run warmer, you can get Lean Codes.

MAF sensor is used by the computer to calculate the 14:1 air:fuel ratio.
If MAF says 14lbs of air comes in computer knows it has to add 1lbs of fuel to get 14:1

If MAF is dirty then it may report 14lbs of air when there was really 16lbs of air
So engine is running 16:1 ratio which is too lean, almost the same as a vacuum leak.
So engine can buck when trying to start off or accelerate, and a lean fuel mix burns hotter which can causing pinging/knocking, also warmer engine temp

O2 sensors tell the computer that engine is running lean, so computer adds more fuel but it has limits because a 3.0l engine can only pull in 3 Liters of air every 2 RPMs, so computer has a sanity check when MAF and O2 sensors are not confirming it's calculations.

Very simple system, don't over think it, computer is not smart, just fast at doing simple calculations