Play-to-Play is a variation of the tried and true Pay-to-Play business model that allows players to earn more subscription time by performing actions in-game. Unlike the Free-to-Play model, play-to-play games are subscription based, meaning if you don't earn the extra time in game you can no longer play the game.
Current games using the Play-to-Play model are EVE Online (using an item called PLEX or "Pilot's License Extension"), EverQuest II (which added the option in late 2011 via an item called Krono), Wildstar (via "C.R.E.D.D." available shortly after release), and World of Warcraft (which added the option via a "WoW Token" on April 7th, 2015 in North America and April 21st, 2015 in Europe). These items allows players to use in-game money to purchase 1 month subscriptions to the game. The items first have to be bought for real money, but can then be sold within the game's marketplace to other users using the in-game currency, meaning there has to be a group of people paying real money for the items in order for there to be any available in the in-game market, which also keeps the prices quite high, but within reach of active players. This also means that every month of game time that is played by a player has a 1:1 correlation with someone somewhere having paid for that game time at some point. That is one of the primary differentiators between this system and Free-to-Play systems.
One of the primary motivations for providing these items in-game is to curb third party gold selling, which can have a negative impact on the in-game economy, can lead to scamming and account theft, is a significant source of in-game chat spam, and can have a negative impact on the gameplay of normal players as these gold farmers find ways to exploit the game which can have a negative impact on server stability or take up in-game resources that normal players could have used. By providing a legitimate avenue to purchase in-game currency for real-world money, these companies hope to greatly diminish the business of the third party gold sellers to the point that it is no longer profitable for them to operate within the game.