Mass Effect 3 is about a war with the Reapers, and as you play the single player game, the people and armies whose help you earn count as War Assets. The game's still story-driven, and it doesn't end until you've completed the main series of missions. But when you do, what happens in the final cut-scene depends on how many War Assets you have accumulated.
That part is kind of cool. But the balance is incredibly harsh: I did every proper quest I could find in Mass Effect 3, made sensible decisions that didn't conflict with my choices in the previous games, and brought people together. But I still got a gallingly bleak ending.
That's because I'd never played the multiplayer. It's a co-op mode where you and up to three other players have to survive waves of AI enemies and complete objectives. If you succeed, you get an increase to your Readiness rating - a percentage by which your single player War Assets are multiplied by. These are specific to each sector fo the galaxy, so if you have a lot of War Assets in the Terminus Systems, you'll gain more by playing on a multiplayer map set in the Terminus Systems.
It's all rather... dirty. Presumably they're trying to encourage you to try the multiplayer because to do well in it, you have to buy or earn unlockable items, and you can get these for real money. But they're doing it by hurting your single player game, slapping a good playthrough with a bad ending as a penalty for not playing co-op. Even if you like co-op, it's not unreasonable to want to play through the single player first.
It is possible to get the best ending in single player without playing multiplayer, but it's twice as hard. All your War Assets only count for 50% of their potential value. The biggest gains in War Assets come from a culmination of your decisions in the previous games and your decisions in this one: if you've helped a race before, and you help them here, it's often possible to get their full support and resolve their conflict to get someone else on your side too.
In other situations, a wrong call somewhere along the line, or a Paragon or Renegade score too low to pick the right thing to say, can mean a character dies, a race is demoralised, and if they fight for you at all they're worth much less to the war effort.
I said I did all the 'proper' quests I could find - if you want to maximise your War Assets without playing multiplayer, you'll have to do the others. The only quests I had left were ones to scour certain systems for planets that aren't marked on your map, scan them, then fire a probe and return to the Citadel. Even compared to Mass Effect 2's resource-scanning, these are dull.
Here's what I recommend: don't. Don't do any quests that are boring, don't play multiplayer if you don't want to, and don't go through old save games trying to optimise your decisions for the most War Assets. Don't let BioWare's seedy design decision manipulate you into playing in a way you don't want to.
If they've made a game that's brutal, harsh and dark if you don't play multiplayer, they've made a game that's brutal, harsh and dark. That's how I reviewed it, and it's still phenomenal.