The Market is where you can buy and sell your players, for profit, and to get the players you desperately need to finish off your squad.
It works very much like an Ebay style market, with the option to bid for players in an online auction, or buy the player now, if you can't stand waiting.
You can also send trade offers of players of equal value. A players' value is mainly determined by their rating and cardweight (how many times they appear in packs).
On the trading forums, you can even arrange trades with other forumers.