The Companion Drone is part of the Companion Gaming mechanic
The Companion Drone is controlled by the Companion App and lets you support your teammates using a tablet such as an iPad. Many support options are available including Healing your allies, Buffing them, Debuffing the enemies, Firing Missles, and more.
EDIT 06/23/2015: Companion Gaming has been canned http://www.eurogamer.net/articles/2015-06-23-the-divisions-companion-app-has-been-canned
