Military Strike is a System Signal Source that contains ships aligned to a Power and the system's defence forces. The Power is trying to prepare the system, by military means, to be able to expand to it.  To locate a system that will have ongoing Military Strikes, you must look at the "Expansion" Section of your Chosen Power, assuming that Power has a combat-oriented Expansion Phase.

When aligned to your Power in a Military Strike you will get 10 Powerplay (bonds) per ship killed.