The term world refers to the domain of discourse, and is often synonymous with the planet Earth. It is sometimes used to refer to the entire Universe, though this use has faded as our knowledge of the Universe has increased.
World can be used in less literal terms; for example, when describing two people with very little in common, one can describe them as "living in two different worlds." When a person refers to the "end of the world," that person usually means "the end of everything I am familiar with."
The terms first world, second world, and third world are used to divide the nations of Earth into three broad categories. Originally, during the Cold War, the "first world" referred to nations within the United States' sphere of influence, the "second world" to nations within the Soviet Union's, and the "third world" to nations within neither sphere. After the Cold War, the "first world" began to refer to countries with "western" societies and large economies and the "third world" to developing countries in regions such as Africa (because originally neither Cold War superpower bothered with such countries); with the fall of Leninist Communism the term "second world" largely fell out of use.
World is sometimes used as a synonym for planet; for example, Mars and Jupiter are two worlds within the solar system. World can also be used to refer to a fictional setting, for example the world of Star Trek or the world of Lord of the Rings.