The observed pattern in which societies move from high birth and death rates to low ones, passing through a period of rapid population growth while the two are out of step. It describes essentially every country that has industrialised, and it is better as a description than as a mechanism.

In the first stage both birth and death rates are high and variable, and population grows slowly if at all. This describes most of human history.
In the second stage death rates fall sharply while birth rates remain high. Population grows rapidly, not because people are having more children but because more of the children survive.
In the third stage birth rates fall. Growth continues but decelerates.
In the fourth stage both rates are low and population stabilises, with an older age structure.
A fifth stage was not part of the original formulation and has been added since, describing sustained fertility below replacement level and consequent population decline.

The age structure changes as much as the size. A society in stage two has an enormous proportion of children; one in stage four has a large proportion of older people. These have different economic implications entirely.
Mortality falls first, and the causes are reasonably well established. Improved nutrition and food security, clean water and sanitation, and public health measures account for most of the decline in the early transitions, with vaccination and antibiotics arriving later and mattering more in the twentieth century transitions than in the nineteenth century ones.

Fertility falls later, and its causes are more contested. The main candidates are child survival, since parents who expect their children to live need fewer births to reach a desired family size; urbanisation, which raises the cost of children and reduces their economic contribution; education, particularly of women, which is among the strongest and most consistent correlates worldwide; the availability of contraception; and changing norms about desired family size.
The lag between the two declines is the entire explanation of the population growth associated with development. It is a transitional phenomenon, not a permanent condition.
The pattern is close to universal. Every country that has undergone sustained economic development has followed this sequence, with variation in timing and pace but not in order.
The compression is well documented and consequential. Britain's transition ran over roughly a century and a half. South Korea, Iran and Thailand completed comparable transitions in a few decades. Later transitions are faster, because the technology and knowledge are imported rather than developed.
The global picture confirms it at scale. World fertility has fallen from around five children per woman in 1950 to roughly two, and more than half of all countries are now below replacement, which is the fourth and fifth stages arriving broadly as the framework describes.
The most serious criticism is that it is a generalised description rather than a causal model. It says what happens, in what order, and does not specify what triggers the fertility decline or predict when it will begin in a given country.
The Princeton European Fertility Project, a large historical study of the original European transitions, found that fertility decline did not track development thresholds cleanly. Declines began at widely differing levels of income, urbanisation and literacy, and spread along linguistic and cultural boundaries in a way suggesting diffusion of ideas rather than a response to material conditions alone. That result substantially weakened the economic version of the theory.
It did not anticipate its own end state. Fertility falling well below replacement and staying there was not part of the original framework, and it is now the situation across most of the developed world and increasingly beyond it. Why fertility keeps falling after the conditions that supposedly drove the decline have been met is an open question.
Sub-Saharan Africa's fertility decline has been slower than projections assumed, which matters greatly for global population forecasts, and the reasons are debated.
The framework was also built on European experience and then applied elsewhere, and the assumption that all societies traverse the same path in the same order has been criticised as importing a particular history as a universal law.
The demographic transition is the single most useful framework for understanding population change, and it explains why rapid growth in developing countries is a stage rather than a trajectory, which is directly contrary to the assumption behind most population-crisis argument.
The current concern has largely inverted. The policy questions now facing many countries concern ageing populations, shrinking workforces and pension sustainability, which are the consequences of completing the transition rather than of failing to.