For example, I was playing Stark and was 4th on Iron Throne. Tyrell was 3rd and it was his turn to play. He attacked Martell and Martell used his Doran Martell card and moved Tyrell at the bottom of the Iron Throne track. This moved me up in 3rd. The result : My turn got skipped and it became Greyjoy's turn, who was the next player after me.
On top of this, Tyrell got the chance to play again in the same turn since he became 6th player on the track.