If I had been paying attention, I would have answered earlier.
The cord in the photo is indeed 'phone cord, and is supposedly 30' long. It will reach anywhere within the layout room, although I generally unplug it to follow a train, plugging it in at various facia jacks spotted around the room. As Michael and Russ have mentioned, it is used in conjunction with an MRC Controlmaster 20, and doesn't carry the power that actually runs the trains.
I can also use one of my SCR throttles to run trains (much finer control), but the hand-held units require an input of AC power (from the AC terminals of a power pack or from a separate AC transformer), which they convert to DC, which is then routed back to the track. I have a heavier cable for these throttles, and use a single, non-compatible output jack near the power source. I suspect that the combination of the cable's wire size, coupled with the fact that I use only a single pair of wires to power the layout, limits the output of these throttles - they will run a single locomotive and its train anywhere on the layout, but if additional locos are required, especially due to train weight, they can't supply sufficient power.
I also have a PWM throttle, but have yet to hook it into a cable system - it offers the control capabilities of the SCR throttles with the output capabilities of the Controlmaster 20. I'll get around to it, eventually.
Wayne