Remember, the Xbox One's new achievement display does more than just look fresher. It also lets multiple people earn separate achievements from within the same game, even logged onto the same console, and display that as its own colour-coded pop-up.
Here's an example, taken from around the 11:15 mark in this video.
You'll notice at the start it tells everyone just who unlocked the achievement, both to save on confusion and, I guess, allow for a little gloating as well.
The colours will change too; while this one is a greeney...bluey...thing, Xbox VP Marc Whitten says that each player's unlock will be in their "chosen color".

Go everywhere with your kids
This must-have bundle nets you either of Gladly’s award-winning Anthem2 or Anthem4 All-Terrain Stroller Wagons as well as must-have accessories like a parent cupholder, a removable storage basket, extra-large canopies, a nap system, quilted comfort seats, a cooler bag with a padded shoulder strap, and a travel bag.
It's not going to change the face of the planet, but hey, it's still kinda neat!