Player metrics is when the game gathers information on what the player has done. Such as how many dungeons they have cleared, how much gil they have spent, how many hours was the player online, and so on.
This used to come almost yearly in FFXI along with the same time as the FFXI census rolled around, but we weren't given one for FFXIV:ARR Census. It was a nice thing to look forward to.
While the achievement logs do record a certain number of things, such as monsters killed, it doesn't provide a log after reaching the highest achievement provided. E.G. There is nothing beyond defeat 100,000 enemies.
Are we ever going to see our player metrics?