Answer:
it's about a man or a women (eg. Fiona Shepard, you can change the name since its an RPG) and you go on a mission to save the galaxy from a corrupt spectre called Saren. You have a crew and a ship called the Normandy SR1. You are given assignments too but the main story is the missions.
Since it's an RPG (Role Playing Game) you can be either nice or nasty(Paragon/Renegade)...Mass Effect characters aren't really good or bad, you're saving the galaxy so technically you are good but you don't have to be nice about it. Paragon is nice/friendly and Renegade is nasty/cruel.
It is hard to explain Mass Effect. You have to play it to understand it.
It is amazing
(go to http://uk.xbox360.ign.com/dor/objects/718963/mass-effect/videos/masseffect_in5min_spc_121509.html for full story)