EDIC stands for Electronic Diesel Injection Control.  On a Toyota is a simple way to turn an diesel engine on and off.  It is also the method which which you use to turn the amount of fuel delievered up and down.  The EDIC is a little elctronic motor hooked up to a relay that is connected to the key position of your truck.  It has three positions: on, off, and start.  In the "ON" position it slides a bar that is connected to the fuel pump to a position that allows the pump to deliever it's normal amount of fuel.  In the "off" position it moved the bar to stop allowing the pump to deliever fuel, turning off your truck.  In the "start" position, which is engaged when you have the key actually running the starter motor trying to start the truck.  The start position allows the fuel pump to be in the "over inject" position allowing each cyl to have extra fuel sometimes required to start the truck.

EDIC is considered somewhat of a more modern diesel engine contraption as diesel engines have been around for a long time and previously the way of turning one off was to cut off it's air supply, like a diesel powered unimog which has a lever.  When you remove the key in a unimog, the truck still runs.  Ironically enough I've rigged my HJ60 to continue to run for a set amount of time after I remove the key to allow the turbo to cool down.  This is done through a turbo timer.

In other more complex systems and particularly computerized and electronic systems, EDIC can plays a more crucial role and is sometimes directly integrated into the fuel pump.