Hi Gene,
As SG says, primarily to control mast pumping... With my deck-stepped mast and single lowers, the babystay alone isn't enough to do so when it's blowing, so an inner forestay and runners add a LOT of security to my rig...
One additional benefit I really like, they can afford a nice handhold when moving about the cockpit of a small boat. Do you have a wheel on your boat? If so, one of the riskiest things you'll do on a routine basis in rougher weather, is having to step up onto the cockpit seats to move aft around the wheel... That's one of the major downsides to a wheel as opposed to a tiller on a smaller boat IMO, but a running backstay is often situated in just the right spot to afford, if not necessarily a secure handhold, at least a very convenient thing to grab onto to steady or balance yourself. Whenever I have to go aft in rougher seas to adjust my windvane, having to step over the control lines to the tiller and whatnot, having the runners in place to grab onto add a HUGE measure of security, as the pic below should illustrate...
You really want to try to take them aft of the sweep of the boom, if possible... On boats raced with larger crews, that's not so critical, but on a cruising boat being sailed shorthanded it's definitely more desirable... Best of all is to have the deepest reef in your main cut so the head of the sail will lie no higher than their attachment point on the mast, so then in heavier weather you can leave both runners on all the time, and the main and boom is clear of them in the event you need to ease the main, tack, or jibe...
best regards,
Jon