In Strife, the Communicator (or Com Unit as it is officially called in the Manual and game) is an item obtained from Rowan after his quest. With this, the player can receive incoming messages from Blackbird and other information.
Blackbird states that the Communicator only works for fully humans, probably as a method to stop the Order from using it to trap The Front. Blackbird can not only send you messages, but can see and hear what you do.
In the Shareware demo, you get the Com Unit from Harris' hidden stash, which may have been stolen from someone at some point.