The major reason for population changes, whether in an individual country or for the whole world, is the change in birth and death rates. The birth rate is the number of live babies born in a year for every 1000 people in the total population. Death rates are number of people dying per 1000 people. When birth rates are higher than death rates the population of an area will increase. This is known as natural increase.
Over the past 150 years improvements in health care and sanitation around the world have led to a drop in the death rate. While birth rates have dropped in MEDCs, birth rates are still high in LEDCs. Therefore the number of people in the world has grown rapidly.
The map below shows changes in birth rates between 1960 and 2016.