In regular parlance it very quickly came to mean countries that are very underdeveloped, with high levels of poverty, simply because this tended to map quite closely to non-alignment.

Unless you're reading something about cold war geopolitics, most use of the term takes this casual meaning, though you can usually get confirmation of what is meant from context.

I don't see it used as much as in the past.

First world countries are developed on an industrial level and a cultural level for personal liberties and democracy. The US, most of Europe, Japan, etc. are all first world countries. Second world are developed industrialy but not so democratically. China and Russia are good examples. Third world countries are those underdeveloped industrially and democratically. Most of Africa and countries in turmoil like Venezuela are good examples of third world countries.