Hearthstone has been in beta since Aug 19, 2013 and is limited to those who have beta keys. Currently October 21, 2013 the game has been in beta for around 66 days and still no word on a release date.
Money
So why doesn't Blizzard release the game to the public yet if it seems ready? It most likely has to do with money. Lets not play stupid the game is making money as it stands right now, I've seen players on YouTube buy 40 packs at a time.
If the game was released to 100,000 players with beta invites then how much money did they make? If each player bought only 1 pack then it would have been 199,900 dollars. 2 packs average? 398,000 dollars. That doesn't even consider the arena money gathered for paying to play.
I would say a rough estimate is that players have spent money on average 5 times. That is a safe assumption it is probably much more than that. 995,000, close to a million dollars from a beta.
The Healthstone game is potentially the most profitable IPO the company has right now. Even if the game is in beta it is making money so it allows them to delay release without too much of the pressures of profit.
Bugs
The game isn't ready for release to be honest.
I have watch hours and hours of the game be played. There are definitely still bugs and the Hearthstone team is a small one so patching and making change is slower than usual. I have seen issues with the cards not displaying correctly (missing card from hand, glowing cards, card hovering over the board) and minions being placed off the board. Also I have seen where the cards do not work as intended, counterspell proc'ing off of a silence battlecry from a minion. Odd things like that make the game close to release but not ready.
Blizzcon
Good news that Blizzard will be showing off the product at Blizzcon with a tournament. They might take the attitude beta is beta but how embarrassing would it be for Blizzard if the game has those bugs show up during a live match in front of their audience? So the game should recieve a huge update fixing all the bugs before Blizzcon if were lucky and thus making us that much closer to a released version of the game.