You get a win screen with the option to go to a new sector by clicking an icon in the upper right of your screen next to the mini map. You get XP and an award cache with a bunch of items. You can immediately move on or finish up unfinished business in the present sector.
You can set the difficulty of the next sector but I don’t recall the details. Others can fill in the blanks.
Edit: Funny thing. I just got a military win in my present game. I thought of your question and so I figured I’d pop in here fast while it was fresh in my mind. :)
Addendum: My experience so far has been to ally with the strongest race and do shit for them for a while. Then you win. I’m sure others will correct me.