in the context of photography, a slave is a device for synchronizing a secondary electronic flash on a primary flash.

As an example, suppose you have three studio flashes, one as a primary light, one to light a background, and a third one as a hair light.

But you don't want to drag around three cables. So you connect (via PC cables) to the closest flash, and install slaves on the other two.
If you are more hi-tech, you can even dispense with the cables, and connect all the flashes to radio slaves: a small transmitter would then be mounted on the hotshoe over the camera, and you could dance around in the studio, all the time being sure of your perfect flash synch.