The Xbox 360's Achievements system made a pretty big impact in the industry, so it only makes sense that Microsoft would tweak it for the follow-up console. The company has given a little insight on how the Xbox One will revise the popular system.
The official site mentions that "achievements are no longer confined to a single game," which means a publisher could grant you an achievement for playing multiple games in a series. Developers can also add new achievements dynamically, letting them refresh a game based on metrics or feedback from the community.
Gamerscore carries over from the Xbox 360 as well, though you can't actually play those games on the new system. The page also teases that you'll get a more detailed look at how you earned your achievements, though it didn't go into detail on that point.