You earn Phantom Cards when you win games. You have a chance to win any card in the game, even rares and odds.
These cards will only last for 20 days or so. Phantom cards have an expiry date, which can be seen from the Army Tab
All players also start with the cards in the Default decks (Sylvan, Mountain Folk, Dark Legion). Unlike Phantom cards, Default cards never expire.
You can use Phantoms in ladder games and other games in the lobby as well as in Constructed tournaments.