Well, third world countries are nations which are significantly behind the "First World" nations in terms of social, economic, and political development or progress. For example, much of the middle east still believes that an imaginary sky-fairy has given them the authority and permission to murder women with rocks anytime the men get upset about something, and they think simply being men gives them the right to rape women. These things basically makes them cave-men.

So "second world" countries are those which are not quite stone-age savage, but are still noticably behind.

So an example of a "Second world" nation would be the United Kingdom, which enjoys many of the modern luxuries of the first world, and much of the social freedoms and progress, and yet still suffers under a completely irrational monarchy and lacks essential freedoms such as the right to self defense. As citizens of the United Kingdom are completely forbidden from keeping arms for the sole purpose of defense of self, family, and property, they are essentially servants of the state. Such a nation cannot then be justly described as "first world", as real first world nations such as the United States have enjoyed these additional freedoms for many generations now.

If my definition is not "official" then I apologize, nobody ever really explained the meaning of the phrases to me and my understanding is simply based on 3 decades of contextual usage. The implication is that there is a single path of progress which all nations are basically following. The first world is setting the example, and the rest are following our lead.

('that we still have such a long way to go is one of the reasons it's so amazing we haven't nuked ourselves to extinction yet :)')