Technically these animations are already possible and available today.
What core animation essentially is, is a set of widgets (not the dashboard kind, the programmer's kind) and functions and objects that automate common animations processes for the developer.
As shown at WWDC 2006, if a developer wants to move a little image from left to right, till now he would have to write an animation program that takes the image and moves it from left to right.
Now you only have to tell Mac OS X the starting point and ending point and a few "stops on the way" called keyframes, and OS X does the work for you.
One advantage is that there will be one interoperable, unified animation acrhitecture, and every developer can and will use it instead of developing their own.
This way, software companies save huge amounts of time, money and fancy Mac apps will roll out faster and special effects will have less possibility of failure, because the animation is managed by OS X, not the App, which may have bugs. (Not that Core Animation will be bug free for sure, but it's just one source of potential trouble and can thus be fixed quickly.)