The whole MOBA/ARTS/Lane-Pushing/nerdrage genre was mystifying to me until I tried DotA 2.

You basically have two teams, three "lanes" between each team's base, and 5 heroes on each side. Both teams' bases send out "creep" waves (basically dumb soldiers) every 30 seconds, and they'll automatically attack each other in the lanes. That naturally results in a stalemate, so the entire game revolves around the actions of the teams' heroes. If you take down their towers and defenses, or sufficiently harass or kill their heroes, your job will become easier. Your ultimate goal is to destroy their "Ancient," which is basically a single, all-important, living structure. Destroy the Ancient and their team loses, hence the game's title.

I highly, highly, highly recommend playing your first game with a RL or online friend who can voice chat you through the basics. A buddy of mine did that for me, and it really helped.

Praz was right that it focuses on managing your specific hero to accomplish your team's goals. So, basically, the better you know how your hero works, the better you'll do. Along with that, the better you know your teammates and opponents' heroes, the better you understand what kind of role you need to play. Sometimes, that means you carry your team with the hero's strong abilities. Other times, you need to support and keep people alive, or distract the enemy in a teamfight, initiate a gank, etc. You eventually learn what gets you more gold, levels, and items faster, and all of that adds up to playing a better game over time.

It is a bit overwhelming at first, and I never though I'd like the genre. However, I started feeling good about the game after my first week or two of occasionally playing. Now that I've been playing for 3+ months, I'm not even interested in the SC2 expansion. It fills my RTS need by being both free and fun. Yeah, there are dropped items and unlockables, but they're 100% cosmetic and yield no gameplay advantages.

I'm also fond of the fact that Valve is developing it, as we know their record for regular updates and incorporating community involvement. If creative players can make money off of people buying silly cosmetic items, I can't bear any ill will toward Valve. It's just smart business.

Lastly, while it's still in "beta" and invite-only, you'll find that it feels like a finished game. The beta is there because they're still adding in some content from the original dota, polishing some of the artwork, and balancing some gameplay details that won't make sense to a new player quite yet.