Initially a person in a swing generates a
torque force on the supporting chains by leaning and pulling or pushing on the supporing chains. This results in the chain becoming offset from under the supporting bar, with a resulting horizontal component of tension that propels the person and swing forwards. This can be repeated to further increase the height of the swing. At some point, if the person stands on the swing, the rate of increase in swing height can be made faster by moving the center of mass inwards (upwards) during the bottom portion of the swing, then outwards at the ends of the swing. An example of the latter method is how this gymnast (Val Dero) reaches bar level after just 3 swings after an initial push, followed by a quadruple back flip.
http://rcgldr.net/real/quad.wmv 
