Before I even begin, let me first notify that the difference is NOT in terms of developed, developing or under-developing countries. The difference is not even in terms of the wealth or power a nation holds. It is not even about the Purchasing Power Parity or Average Income Per Capita. So what is this 1st, 2nd and 3rd world is all about? Well, the answer is associated with war, Cold War to be more precise. Cold war was basically, a state of political and military tension after World War II between powers in the Western Bloc (the United States, its NATO allies and others) and powers in the Eastern Bloc (the Soviet Union and its allies in the Warsaw Pact). First World comprises the United States and United Kingdom and their allies, the Second World the Soviet Union and China and their allies, and the Third World the neutral and non-aligned countries. Basically Third world was that which neither participated nor interfered in the war. This was the real definition of the First world, Second World & Third world countries. 
Blue – First World
Red – Second World
Green – Third World
Now over the time, first world became superpowers with economical advantages with innovation as the prime focus, the second world are a bit lesser in both aspects (not to be confused with military), and the third world are those who are basically exploited with corruption, apathy but growing to meet the international standards of developing nations. So whenever a country is being pointed as a third world, it does not means that it is not developed or lack in the basic necessities but is actually a country which neither took part in war, nor helped in it. image source
