During the Cold War period Third World referred to countries which didn't align themselves to either of the power blocks the US and its allies and the Soviet Union and its allies. These nations formed the non-aligned movement. It was usually applied to the mostly developing nations of Africa, Latin America, and Asian countries.
Since that time, third world refers to developing and undeveloped countries which have large scale poverty and low levels of economic development. Third world countries often have dictatorships as the form of central government, and in many third world countries government corruption is rampant.