I credit my ability to quickly grasp the mechanics of Hearthstone to the game's animations. The animations do so much more than making the game visually interesting, they make it easy to understand. For example, cards that are exhausted for the turn display "zzz..." as a sign they are resting. Also, when a paladin plays his Divine Shield card, an actual golden bubble appears around the protected card and stays there until it's destroyed. Everything in Hearthstone is really obvious, and that's great because it allowed me to focus on my strategy from the very first game I played. It's not like StarCraft 2, where you can spend months just trying to master the controls of the game.
After losing my second game (though not as badly as the first) I started to realize that I really wanted to build my own deck. I kept seeing my opponent play cards that I wanted to use, while my own deck seemed to be filled with junk that only staved off my inevitable demise. A lot of that was probably bad luck, but given the opportunity to build my own deck I'd definitely take a different approach to whatever stupid Anduin was doing. (Did I mention I irrationally hate Anduin?)
Anyway, I only bring this up because I'm usually pretty content to work with what I have in games. I don't often need more and yet here I am, already wanting more cards and looking at Hearthstone like a blank canvas. Maybe I can swindle a beta key out of someone before PAX is over ...
Beyond the gameplay, I also found Hearthstone visually stunning. The art and animations are obviously well done (it's Blizzard, after all) but the vibrancy of the colors really draw your eye. I could see myself playing this on the subway and having everyone around me looking over my shoulder. I especially love the animated play mats, which feature different locations in Azeroth like Orgrimmar or Pandaria. I hope they'll eventually add one for all the zones in World of Warcraft.
So, my first impression after playing? Absolutely positive. Seeing how accessible the game is, I'm most excited to share it with other people. I have a lot of friends I like playing console games with, but I can't play games like WoW or StarCraft 2 with them because they take too much time to play with any degree of competency. Hearthstone would allow my friends to play something with me without a huge investment of time or demand for skill. From the other turn of the coin, I'd also love to play this game with my friends who are highly competitive Magic: The Gathering players. To them I'm betting Hearthstone would be to Magic: The Gathering what League of Legends is to Heroes of Newerth or DotA 2: a competitive game with potential for hardcore competition but designed with casual players in mind.
Now I just have to wait for beta.