Not to be confused with Mao Zedong's Three worlds theory.
The three-world model was a model originally used in the imperial core to classify countries on their allegiances during the first Cold War. The model persisted until the overthrow of the Soviet Union in 1991 and has since taken another meaning related to the supposed wealth or development level of countries.
Original model
Originally, the model categorized countries depending on their allegiance towards either NATO (the first-world), the USSR or Warsaw Pact (the second-world), or those that remained unaligned or enjoyed relations with both powers (the third-world).
Modern usage
Nowadays, the model is used by the bourgeoisie to enforce their own post-colonial mindsets on countries of the world, haphazardly categorizing them in terms of economic development and standards of living for the population.
The first world encompasses (Western) Europe and North America, as well as their dependencies (such as the Republic of Korea, Taiwan province...). They are considered to be the richest nations on Earth or those with the highest standards of living, actually forming the imperial core.
The second world encompasses emerging or developing countries, although this category is rarely used. China, Russia and India might be considered to be in this category as strong emerging economies (despite China being the first country in the world in terms of GDP normalized to purchasing power parity, the country is still considered to be an emerging economy at the UN).
The third world, by definition, represents all countries that are in neither of the two other categories. These would be the poorest countries in the world or, since capitalism considers that democracy equals wealth, the "least democratic" countries.
The new model thus becomes a loaded term, and leads to elitist thinking in the imperial core that the rest of the world is not as developed as them and thus not as culturally "advanced".