The Demon Hunter addition is a big deal for Hearthstone, as it will be the first new class introduced since the game's launch, and it will be free to all players. You will need to unlock it though, by playing the free prologue.
The prologue is now available and it will take you through Illidan Stormrage's origin story while showing you the Demon Hunter's mechanics. After the prologue, you will have the Demon Hunter class, Illidan Stormrage Hero, 10 Demon Hunter Basic Cards and 20 Demon Hunter Initiate cards.
The Demon Hunter class will become available in regular play on April 7, the same day the next expansion, Ashes of Outland, is launching.