A Military Strike is a Powerplay-related System Signal Source specific to both Zachary Hudson and Denton Patreus. It is similar to a Conflict Zone, but contains ships aligned to a Power battling against a system's defense forces. At these sites, the Power is trying to prepare the system for its expansion there through military operations. When aligned to a Power conducting a Military Strike, pilots will receive 10 Powerplay (bonds) per ship killed at that site.
To locate a system with active Military Strikes, check the "Expansion" tab of either Zachary Hudson or Denton Patreus in the Galactic Powers menu.