Breaches through the enemy hull and wreaks havoc. Awesome.
Boarding Drones are used to board the enemy ship without risking your crew. Boarding drones have the same amount of health and attack as a Rockman, and will fare similarly in battle. A Boarding drone always causes a hull breach in the room it lands in, however the drone doesn't require air and will remain active unless it is destroyed or loses power. The drone is automatic and cannot be controlled by you. This can often result in them picking the wrong fights and ending up dealing less damage to the enemy ship and crew than a controllable boarder could. The upside of the drone is that you can keep sending more of them over as the enemy crew kills the last (at the cost of another drone part of course). The best strategy if you wish to use such drones is to have a weapons system strong enough to punch through shields and destroy enemy weapons and medbays. Then send the drone to kill the crew and rake in the extra resources you get for keeping the enemy ship intact.
Note that the Basilisk variety of the Mantis Ship is the only type that starts off with a boarding drone, the scematic for it is exceedingly rare and might not show up in stores at all in a given playthrough.