Nearly every country has a stock market, but to make it easier for investors to understand what they're getting into, the industry has carved them up into three groups - developed markets, emerging markets and frontier markets. The names (for once) are quite helpful.
The divvying up is not just based on the economic development of a country but also the size of the stock market and how easy it is to trade.
Once an emerging market, such as Thailand, Brazil or Russia, improves on those measures, it secures promotion. In the case of Greece, it suffered relegation from "developed" to "emerging" in 2013 following a debt crisis (which was the least of its worries). The important bit for investors to focus on is that emerging market = higher risk but potentially higher rewards (returns).