Extraction Facilities are a diversion in the game where you must enter a building and capture three control points without the enemies recapturing them. To capture a point, all you have to do is stand on them until the meter in the upper left is filled, then you can move onto the next one.
The trick with these Extraction Facilities, of which there's four in the game, is to take out all of the enemies inside first. More enemies won't show up, due to it being a closed off building (some might manage to glitch inside), but once you clear all of the enemies, it will be easy to capture the control points. One thing of note is to leave one or two Extraction untouched to try for the Terminal Hog trophy/achievement .