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 depend on this for effects to resolve during later turns after the card was initially activated. Several examples of such cards include "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 otherwise affecting the Duel. A card that counts phases rather than turns (such as "Dust Barrier") cannot be moved forward by "Pyro Clock of Destiny" (as the 'skipped' turn is considered to have no phases in it).