To expand slightly, you can win each sector (like a town in Din's Curse) in a number of different ways -- all the remaining races being allies, completing actions that give you Legend points (destroying bosses, exploration), completing actions that give you Fear points (destroying race ships and planets), etc. You can win a sector via any of these means, but depending on the races in play and their attitudes toward each other, some of the victory conditions can be very hard or impossible to attain.
The Drox guild also sometimes asks you to keep certain races alive or destroy them, and you will get bonus loot at the end of a sector if you complete these optional objectives.
With the IotA expansion, (among other things) the Drox guild can also give you objectives that you must fulfill or you lose the sector -- getting a particular race to be most powerful, getting two races to be allies, etc. These can be particularly brutal sometimes. IotA also introduces persistent galaxies, so if you can kill off races or have new subraces emerge, and it has a chance to be carried to the next sector.
But as far as "story" goes, there's just the background about the Drox and you're an individual mercenary -- the rest of the "story" you can create yourself through your actions and the events in the 4x game happening in each sector.