The term is said to have been coined by American sociologist and demographer Kingsley Davis. It was in fact used earlier by George Stolnitz, who stated that the concept of a stationary population dated back to 1693. A mathematical description was given by Mirrlees.
In the long term zero population growth can be achieved when the birth rate of a population equals the death rate. (This ignores migration, which is valid for the planet as whole, but not necessarily for a nation.) However, a population that has been growing in the past will have a higher proportion of young people. As it is younger people who have children there is large time lag between the point at which the birth rate falls below the death rate and the point at which the population stops rising
Zero population growth is often a goal of demographic planners and environmentalists who believe that reducing population growth is essential for the health of the ecosphere. However, achieving ZPG is difficult because a country's population growth is often determined by economic factors, incidence of poverty, etc.