In Hearthstone: Heroes of Warcraft, Arena Mode is a PVP mode where you make a deck out of a random draft and try to win as many games as you can with it (kind of like a MTG draft game).
When you first start playing the game however, all you have access to is the Practice mode.
To unlock Arena mode, you just need to defeat all of the different classes at least once in Practice mode.
Once you get good at playing all of the different classes, Arena Mode can actually be an affordable way to get card packs, since the more games you win in an Arena match, the more rewards you get from it.
