By its literal definition. First world describes the US and its allies, the second world described the Soviet bloc, and the third world is everyone else/the non-aligned nations.

Here's Wikipedia. It's not my definition. I'm also not saying people haven't used it in a derogatory way now as a term to refer to underdeveloped nations.

The term Third World arose during the Cold War to define countries that remained non-aligned with either NATO or the Warsaw Pact. The United States, Canada, Japan, South Korea, Turkey, the Southern Cone, Western European countries and other allies represented the "First World", while the Soviet Union, China, Cuba, North Korea, Vietnam, Romania and the rest of the Warsaw Pact and their allies represented the "Second World". This terminology provided a way of broadly categorizing the nations of the Earth into three groups based on political divisions. Due to the complex history of evolving meanings and contexts, there is no clear or agreed-upon definition of the Third World.[1] Strictly speaking, "Third World" was a political, rather than economic, grouping.[2] Political alignments in Europe during the Cold War after 1961

Since most Third World countries were economically poor and non-industrialized, it became a stereotype or a derogatory euphemism to refer to developing countries as "third-world." In political discourse, the term Third World was often associated with being underdeveloped. China was labeled "Third World" for several decades in the 20th century before its robust development in the 21st century. Some countries in the Eastern Bloc, such as Cuba, were often regarded as Third World. The Third World was normally seen to include many countries with colonial pasts in Africa, Latin America, Oceania, and Asia. It was also sometimes taken as synonymous with countries in the Non-Aligned Movement. In the dependency theory of thinkers like Raúl Prebisch, Walter Rodney, Theotônio dos Santos, and others, the Third World has also been connected to the world-systemic economic division as "periphery" countries dominated by the countries comprising the economic "core".[1]

In the Cold War, some European democracies (Austria, Finland, Ireland, Sweden, and Switzerland) were neutral in the sense of not joining NATO, but were prosperous, never joined the Non-Aligned Movement, and seldom self-identified as part of the Third World.

Since the dissolution of the Soviet Union and the end of the Cold War, other terms have also been used instead of Third World such as developing countries, least developed countries or the Global South.