Saren, a rogue spectre (think sci-fi James Bond) was brainwashed by a Reaper (evil race that wants to kill everyone) into rallying the Geth (isolated robot race) to bring the Reapers into the galaxy. Shephard found out about this, became a spectre, and kicked Sarens ass before he could finish his evil plan. That's pretty much all you need to know, I think.
Oh, also the council are all deluded idiots refused to believe Reapers exist, and Shephard may or may not have allowed them to die at the end of Mass Effect 1. If they didn't die then they somehow remain as dumb as ever (and continue to believe that Reapers don't exist), and if they did die then they are immediately replaced by a new council that is equally thick.