In stage 1 death is caused by starvation, disease, and the general danger of living in the world of pre-history.

In stage 2, which occurs as agriculture becomes more organized and at least general medical knowledge is starting to diffuse as people begin to live in larger settlements, food supply improves and death rates drop, while the birth rate remains constant. It's the gap in birth and death rates that causes the population to balloon here. (My kids sometimes have trouble with this and talk about how birth rates drop too, which isn't the case. Death can still be the result of influenzas or other fast moving diseases, but survival rates for these improve throughout the stage. Infant mortality drops here too.

In stage 3, as societies continue to advance and medical care improves drastically the cause of death is more likely to be old age or progressive diseases like cancer. Birth rates are dropping by choice as people realize they don't need to have 6 kids to ensure that 2 survive to take care of the parents, and death rates continue to decline.

Stage 4 is marked by an increasing death rate as a result of the aging population - cancer, heart attacks and plain aging hit the top tiers of the population pyramid, and you see zero population growth as the birth rate roughly equals the death rate.