The system keeps track of the total number of quests in the world you have completed, and the percentage thereof. Some players are so old and jaded they spend their time trying to complete every single quest in the world. This includes the first completion of repeatable quests (Daily and Public).
At least once during the early life of this game, the Completion counters were all wiped and reset to zero, making it possible for older players to redo an already completed non-repeatable quest for experience.
To see your Player Stats and Server Ranking, you can press NUMPAD 9 to open the Server Ranking UI, then if you choose "Quests->Quests Completed" you can see your Total Quests Completed and where you rank with other players on your server.