Sway is caused by an unstable oscillatory (under damped) mechanical system
This is not the cause of sway, it is the definition of it. When that system is not in motion, there is no sway. Something must cause the oscillation. Sway can be caused by a number of forces:
Towing Speed - The speed at which you decide to tow your trailer may be the single greatest factor in controlling trailer sway. Any speeds greater than 45mph tend to allow almost any trailer to begin to sway. With traffic traveling at much greater speeds it isn't practical, and most of the time illegal, to travel at a speed that will control trailer sway. (would like to hear from people who experience sway at speeds lower than 45 - I don't)
High Winds
Gusting Winds
Bow Wave - A bow wave is a wind produced by a large semi-truck, box truck or van pushing its way through the air on the highway. This wind travels around the truck and down the sides creating a wind disturbance in the adjacent lanes. This wind disturbance creates a sudden high to low pressure in the air traveling down the side of your trailer. The bow wave, as with the other wind disturbances, creates a tow angle by pushing the trailer and pivoting it on the hitch ball. The bow wave produces a "sucking" feeling in some combinations that feels like the entire tow combination is being pulled into the other lane. (this is exactly what I experience and yes it is sway)
Bad Roads
Downhill Travel
Poor Trailer Design
Improper Loading
Poor Weight Distribution Hitch Adjustment