M.M.O.R.P.G. is an abbreviation for the term Massively Multiplayer Online Role Playing Game. The definition of massively multiplayer depends on the publisher, but the majority of these games hand thousands if not tens of thousands of players on a single server at one time, often times having a multitude of servers to handle all of the players.
The first installment of Final Fantasy that qualified as an MMORPG was Final Fantasy XI which has a total number of players that hovers just above a half a million divided between 20 odd servers. Final Fantasy XI was the first true MMORPG to be spread across multiple languages and multiple platforms (PC, PlayStation 2, and lastly, the Xbox 360).
A second MMORPG installment, Final Fantasy XIV, was released for the PC in September 2010 and remained live until November 2012. The game was later relaunched as Final Fantasy XIV: A Realm Reborn for PC and PlayStation 3 in August 2013, and launched for the PlayStation 4 on April 14, 2014.