User blog comment:Kogath/Monster Hunter: World Discussion/@comment-6050823-20180122033541/@comment-26421638-20180123083445

^ they're some kind of Achievements (That's were they're called on xbox or other media) or Objectives that can be collected by completing some tasks in game, however they can be checked both in-game or even outside the game and they're synchronized with your PSN Account (in case of PS4).

In previous MH games there was something of similar, the Awards on your Guild Card were the closest thing to Trophies/Achievements.

Also, Achievements from Steam (PC), Play Games (Android) or Game Center (iOS) works on ghe same way, and i woudn'tbe surprised if PC version of MHW uses Steam's Achievements instead of Trophies (If MHW for PC will be released on Steam)