Also called convergence, the "catch-up effect" is an economic theory that suggests the per capita incomes in poorer countries will tend to grow faster than the per capita incomes in richer countries. As poorer countries develop quickly and richer countries develop slowly, the poorer countries catch up to the richer, and incomes converge.
Relative Growth of GPD
When a country is poor, becoming a little richer (increasing per capita GDP) is easy, but when a country is already rich, becoming more rich (increasing GDP) gets difficult. Both countries become richer, but the richest countries grow at a slower rate. This is the principle of diminishing returns.
Developing countries can take advantage of the effort richer countries have expended during development by copying production methods and technology. They can skip over technology that is becoming obsolete, thus saving money. For example, developing countries do not need to spend millions to lay copper wire for telephony infrastructure, as the richer countries have done. They can skip directly to cellular telephony.
Growth Must Come from Something
Simply being poor does not mean that a country can grow rich and converge with the rich, developed countries. A poor country needs some kind of impetus, like sudden discovery or development of natural resources, new laws that successfully encourage trade, or investment in health or technology to improve the lives of the people and allow them to focus their efforts on production rather than survival.