Yes, it's an online card game, made by Blizzard. I hesitate to call it a trading card game, though, because you can't actually trade cards.
At it's core, it's kind of a simplified (I'd argue in a good way) version of MTG. I've never played MTG, but I played Yu-Gi-Oh (not at any serious level) for years, and I find the rules and cards of Hearthstone make it a better game. It also helps that you always have someone to play against, and that you can opt out of the pay to win model by completing daily quests and/or doing well in the arena (randomized draft). It certainly takes a long time to collect a good enough base of cards to do well in constructed games if you don't buy packs with real money, but it's satisfying.
