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".
It's not going to change the face of the planet, but hey, it's still kinda neat!