The Xbox One introduces a new kind of No-Prize to lust after and work towards in the form of challenges, which will co-exist alongside plain old regular achievements. Challenges are only available for a while and can be more varied--perhaps spanning games or challenging a whole community--Microsoft has explained in the sort of excessive detail one would expect from a newly-revealed console.
Don't worry: challenges don't contribute to Gamerscore, so your precious measure of personal value won't be harmed if you are, say, in a coma for a month and miss a challenge, Xbox Live Achievements program manager Cierra McDonald explains. However, they can still offer the same bonuses as achievements: a nice little icon, and potentially unlockables.
And yes, as MS has made quite clear before: your Gamerscore will carry over.
Challenges are far more flexible than achievements, able to span multiple titles or count the contributions of every player (McDonald gives the example of a challenge for one million headshots in a game over three days). While achievements are set in stone as ever, developers can add new challenges as they please, potentially reacting to how people play.
"Let's say a certain game is known on community forums to have a fun little sub-game of kicking chickens. Wouldn't it be amazing if the game developers noticed the community enjoying an unintended aspect of the game and creating a challenge around it, with a reward to boot?"
Anyway, if you're an obsessive achievement hunter, do check out the full blog post.