As the only melee weapon available to the Xenonauts, the Shock Baton provides a valuable, but risky, alternative to Stun Grenades in stunning alien troops. Simply put, the soldier using it must run up to the enemy and smack him with it - potentially taking reaction fire from every enemy present, and exposing himself to follow-up attacks should the stun fail.
The Shock Baton is a one-handed weapon, and thus can be paired with a Combat Shield, a Pistol, or grenades. Not counting the necessary TUs to get to the target, it costs 20% TUs to attack - typically allowing a second or third attack should the first fail. It causes a tiny amount of kinetic damage (you DID just smash the alien with the baton), plus a substantial stun effect.
Note that the Shock Baton is useless against robotic enemies like Androns and Light Drones. This is despite the interface showing stun damage being taken by such targets (blue numbers rather than a 'resisted' indicator).