Flashpoints are special areas in the simulation that are controlled by the Zin, where you will find a large collection of them guarding it. They are marked on your map as a red icon with a fist in it and there's a total of 32 across the game's world. To mark it as complete, all you have to do is kill every single Zin that is marked.
There are a few Flashpoints that have some extra combat to them, as after clearing all of the Zin, a Warden will drop down. These Wardens have their full range of super powers, as well as the shield that must be disabled by using your own powers on it. For reference, the Wardens will have Blast, Stomp, and Telekinesis.