The term "Third World" is somewhat out of date now for at least a couple of reasons. However, it is generally used to refer to countries that are very poor and underdeveolped.
The term was first used back in the Cold War. At that time, it referred to countries that were not part of the First World (the rich, capitalist/democratic world) or the Second World (the poorer communist world). The rest of the world was all lumped together under the term "Third World."
From there, the term gradually evolved to refer to those countries that were poor and underdeveloped. Social scientists are somewhat reluctant to use the term today because it seems judgemental. The more common term for what used to be called the Third World is "developing world."