Sway is the uncontrolled side to side movement of the trailer trying to take the tow vehicle with it. Worst case, it would start and escalate back and forth until the setup jack knifes....not a good situation. Sway can happen to any setup, but is more likely with a long trailer and a short wheelbase tow vehicle. This could be bad in a panic stop for any trailer towing setup, but especially bad with a long trailer and a short wheelbase vehicle...... the trailer is trying to push the tow vehicle.......the tail wagging the dog. A sway system stiffens up the connection between the 2 so that the side to side escalation would be more difficult to happen. You can feel the trailer push the tow vehicle in cross winds, and also when a semi speeds by. The bow wave of a semi will push the back of the trailer away from it, but the tongue of the trailer moves toward that lane.....that is what you hear of being sucked into that lane. Even under perfect conditions, a little steering adjustment is usually needed to correct that.
Here is a good primer for Equalizer:
I use the Reese Straight Line with my 29 foot trailer.
Oops, Wayne posted while I was composing, but we are saying the same things.