The turn count (ターンカウント Tānkaunto) is the number of turns in total that have been played in a Duel. Certain cards depends on this for effects to resolve after the card was initially activated. Several examples of that cards that use turn counts to work are "Final Countdown", "Lightforce Sword" and "Swords of Revealing Light".
"Pyro Clock of Destiny" is a unique card that allows the turn count to be increased by one turn, without affecting the duel. A card that stays on the field for a number of phases (such as "Dust Barrier") cannot be moved forward by "Pyro Clock of Destiny".