What contributed to an increase in world population in the twentieth century?

There are several reasons, which have all resulted in more births and fewer deaths.

Infant mortality has fallen in many countries and older people are living longer, due primary to improved medical care. The pressure to have many children still exists in some countries, in order to provide parents with a greater chance of adult offspring. Modern disease control and improved agriculture have reduced the Death Rate from epidemics and famine. Global conflicts no longer kill off sizable numbers of adult men.

With fewer deadly plagues, fewer deadly famines, and fewer deadly wars, populations in underdeveloped countries will increase, even while effective Birth Control lowers the Birth Rate in developed countries.