Villain sectors are limited time missions that you get from the two faction leaders in the Helicarrier and Ant Hill outposts. You can find them by pressing up on the D-pad.
You (are supposed to be able to) pick up 1 per leader, per day, for a total of 2 per day. (Right now it looks like they are resetting everyday but you cannot pick them up but every other day. Not sure if this is intentional or jus a screw up.)
These quests are a higher power level and require you to fight through a level to a boss fight. You can track these missions from the objectives tab in the pause menu and they will be marked on the war table with a green cross hair.
In the Helicarrier, the Shield faction leader, Alisande Morales is located in the top of room with the war table.
In the Ant Hill, the Resistance faction leader, Sarah Garza is located in the big room at the wall directly behind the hero changer when you walk in.