In a nutshell, it's a graphical depiction of the usual M:TG card game, with a little turned based strategy mixed in.
I think that description simplifies it a bit. A lot of the terminology is the same, but it plays out much differently than the card game. I played through the very brief tutorials and then through the chapter 1 solo play. Chapter 1 was almost mind-numbingly easy and was completed in about an hour. I hope the other solo content is longer. I'll probably buy chapter 2 just to see. I have 550 Sony Cash. I don't know where it came from, but I have it.

Turning Debris' statement sideways, it's basically a turn based tactical combat game with MtG flavor. Your planeswalker and summoned creatures have damage, defense, attack range, movement range, initiative (or something like that) and potentially special abilities. If an attack is made in melee, the opponent can counter-attack if they are not defending (ignoring vigilance). This simulates the attack/defense matchup in the card game, but not exactly. If you kill the opponent it does no damage to you. Also, damage to creatures is not healed between rounds, it carries over. There is no counter-attack to ranged attacks. Also, attacks can be crits and do extra damage, so just because a 20 attack mob is attacking your guy with 30 health left, you aren't necessarily safe.
Speaking of rounds, there aren't really rounds, each mob on the field has an initiative that is used to set order of action. Faster mobs will get turns more often. The left side of the screen shows the order of action and it's important to keep an eye on it.
You generate increasing amounts of mana each turn based on the balance of your deck. Mana is very predictable, you'll never be mana screwed.
As debris stated, this will get expensive if you want more color options. The starter decks are all 2 color decks and you will get a couple new cards from the free campaign, but after that you are spending money to get more cards either through boosters or the auction house. They call it an auction house, but it looks like straight sales.
Single Player content. As I said before the free chapter took about an hour and was really easy. Each chapter appears to have 5 missions and a card reward at the end. They are $5. For that price I hope they start taking longer. The card reward is not tailored to your colors. The chapters are sequential, you must buy and complete the prior to do the next.
Talents. Your planeswalker has talents similar to diablo or WoW. When I hit 6th level I got a talent point. The talents are incremental improvements, but I could see high level characters having a significant advantage. 10% chance for green summons to do 10 extra damage on attack isn't huge but add that to a bunch of other talent points and you can see where this is headed. Talents are organized by color so you should probably focus on one, which may be another reason why you wouldn't branch out in decks of other colors. This could have a serious impact on drafts. I may be very strong on white, but I'm not seeing white rares in the draft, what do I do?!
That's enough for now. I did friend Hark last night but after I finished the tutorial and campaign he was gone. I haven't tried any multi myself. I'm guessing he has. I also saw he had something on the auction house, so I'm guessing he can tell us if boosters look like the card game boosters.

I'd love to see trading in the game, instead of the auction house.
I played a bunch more over the weekend and I even spent some money on it to see a bit more of what's available. On the single player side, I bought all the available chapters and I definitely ran into more challenges a bit later on. I also bought some packs so I could try a draft tournament.
The draft was a disaster. I put together a pretty decent white/green deck (25 card minimum - not as small as it seems since there are no lands), but as soon as I started building an advantage in the first match I got a message that an error had occurred and I had to restart to continue. The game was broken. I could navigate the interface, but nothing I did had any effect. The second match I played to completion, but got raped by a black/blue deck that managed to keep my 60/100 elite archer from killing anything. Did I mention that I love the elite archer?
There was no third match and I think there was supposed to be. No idea what happened there. It seems like it's just plain broken.
I sold a couple of the cards I got in the draft on the auction house for enough gold to play a couple more drafts, but given what happened, I don't think I'll try that until I see a few more patches. Also the draft time limit is SHORT if it's your first draft. 30 seconds goes by way too fast when you have to scroll down to see the cards and click on each card to see the details if you don't know them by the name.
I'm half way through the final single player chapter and once that's done I'm not sure what else I'll be doing. I have a few folks on my friends list, but other than knowing they are online I don't know what the list is doing for me. I can't challenge from the list or message from the list, the only option seems to be "remove from friends list". Gee thanks. I'm not sure there's even any direct chat option. I guess I should look for some documentation.