Mass Effect revolves around humans entering the galactic stage. Your character "sheppard" is the first person who is proven worthy of being a Spectre. Spectre's are judge, jury and executioners. They have full use and authority of galactic law.
Utilizing a few characters you uncover a plot by a rouge Spectre to use a Reaper to destroy the galactic federation. Your journey is essential to track him, take him down and prevent the reaper from destroying the leadership of the galactic federation.
Mass Effect also hints at external influences that you really don't interact with but are told are out there. This is to help set up mass effect 2.
There are of course lots of big things to know, but this will give you a foundation of who you are and what you did in the first game. If at all possible I strongly suggest playing the first game before 3 comes out because IDK what you might miss if you don't know the whole story.