When pulmonary embolism happens in the lungs, what makes it so fatal?

Several things: A massive pulmonary embolus will essentially block most of the blood flow from the right ventricle to the lungs, preventing blood from getting oxygenated while putting a huge strain on the right ventricle. Since blood is then blocked from getting to the left side of the heart, systemic blood pressure severely drops along with oxygen delivery and things rapidly go down the tubes.

Heart stops: The problem with pulmonary emboli is that the blood clot obstructs the blood flow through the lungs. So the right side of the heart tries to pump blood through an obstructed pulmonary artery and it cannot. Thus the right heart of the heart stops and the patient's blood pressure drops and the patient collapses and dies. Pulmonary emboli are really dangerous.