It plays similarly to Magic: the Gathering, but with a lot of differences, if that makes sense. (I could list the differences, but that would be a wall of text that wouldn't convey much meaning without more details.)
The main thing to note is that in-game gold can be earned both by winning normal matches and by doing daily quests. Furthermore, daily quests seem to exclusively involve winning matches under certain circumstances, which overlaps nicely with the 10-gold-per-3-wins thing that's always on.
Gold is used to buy booster packs, and also to enter the Arena - an asynchronous tournament similar to what SolForge uses - which guarantees a booster pack as a final prize, even if you completely wash out, so it's never really a waste - though one doesn't keep the drafted cards, just the after-tourney booster & possible other prizes.
I also like the way that they do classes: Each deck starts w/ a class, which has its own unique once-per-turn 2-mana ability, and the available cards are those specific to that class or the large set of neutral cards. This allows each class to feel different, not just because of its ability, but also because of what cards are available to it. For instance, it looks like only the Druid has any kind of mana acceleration available to him, while everyone else has to just gain 1 per turn until hitting the universal limit of 10. Warlocks have Demons, Hunters have Beasts, Priests get lots of strong 1-off effects, Paladins suck, Rogues stab, etc. I assume that this also somehow correlates to what they do in WoW, but I've never played that, so whatever. Though, I do apparently get a free mount if I ever sign up for it.
So, that's my overview of Hearthstone: quite fun, pretty addictive