It's a bit of an arrogant naming system. The first world is considered the countries where welfare, science and justice are said to work properly, maybe a few tiny issues, but overall, everybody has the same rights, no ridiculous excesses between rich and poor, lots of knowledge about science, having well working technology etc. In 2nd and 3rd world countries this would all be less well organized, more corruption and a lower standard in which civilians live... It's today a bit of a classification.
Europe is therefore considered first world... It's also where the term was invented, so first world to be discovered... 2nd world came next and 3rd came third, but that order holds today little significance, as it's rather a classification in how well countries function today, int he standards I just named. Many African countries are considered 3rd world due to loads of poverty, corrupt governments, not a very well working justice system, sometimes even criminals ruling the nation in stead of the government.
Now I am not quite sure if these terms are still official. Like I said, they are a bit arrogant, and what belongs to what is sometimes a matter of interpretation. Many people call the U.S. a 3rd world country pretending to be a 1st world country. Explaining their motivation would exceed my character limit I'm afraid.
I don't like these names myself. They imply the European civilization and culture is superior to the others, and also makes me feel we look down on others. In the media I hear the terms less and less, and likely because of the same reason why I don't like these terms.
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