Population growth seems to be associated with specific societal and technological conditions. The main limitation on population growth is what is known as the "carrying capacity" of a given area of land. In animal populations, for example, the existing vegetation can only support a certain number of animals; if population expands beyond that, more animals will starve. Thus, in nature, populations tend to attain equilibrium.
For human populations, technological innovation can expand lifespans and increase food supply, allowing population to grow. One of the first instances of this was the neolithic agricultural revolution, when people first domesticated plants and animals, leading not only to population growth but to increased population density. Subsequent improvements in food production, storage, and transportation have enabled increased population growth. At the same time, improvements in medical technology have resulted in lower infant and maternal mortality rates.
However, as societies become wealthier, having children changes from an economic advantage to an economic disadvantage. On a farm, 5 or 10 children mean more labor available to tend crops. In a modern wealthy society, putting one child through college is all most families can afford. Thus in most rich countries, including all of Europe, Japan, South Korea, China, Canada, and the United States, fertility rates are below the replacement rate, meaning that unless compensated for by immigration, population is falling. Although the earth's population is still increasing due to high fertility rates in poorer countries, as poverty rates decline, population growth slows.