It's an online game, unfortunately no offline mode. You start off with a krappy little tank of one of the six nations in the game (your choice). The computer matchmaker puts you in games with 15 players on each side. As you play you get experience and silver which enable you to buy better stuff for your tank like bigger guns and engines and ultimately a bigger better tank. There are ten levels or tiers of tanks from tiny between the wars tanks at Tier I up to massive Cold War machines like the M48 and T-62 at Tier X.
It it free to play as much as you want but you can spend real money aka gold as sorta an 'easy button' in the game. Some people yell cheating but it really doesn't help to spend piles of real money if you still don't know how to play. At higher levels, around Tier 7 or so you pretty much have to either use real cash or run lower level stuff to make cash since repairs cost a greater amount of in-game cash (silver) than you can win unless you're really, really good.
I've been out of the game for a few weeks now, kinda burnt-out on it. Biggest annoying thing is it's a team game, and if you get stuck with 10 or so idiots on your 15 person team no matter how well you and the better players on your team do you're screwed. You don't really lose anything with a loss unless you're Tier 7 or higher but still I get too frustrated with the game.
All in all it's worth trying, since it is free at low levels you can see if you like it. And it is still pretty cheap, I've spent maybe $60.00 bucks for over a year playing so far. I really didn't need to spend that, you can buy cool camo to 'pimp out' your tanks for example.
If you want another look before downloading, enter 'WoT' or 'World of Tanks' in YouTube- there are hundreds of demos from the company and 'how-to-play' flicks etc that show how the game works and will give you a better idea of what to expect.