You’re right. Fading in a new background color when you hover over a link could be implemented just as well without an animation by setting a simple transition on the element.
So in this simple example the animation might seem like overkill. But if you were doing something more complex (e.g., changing multiple style properties at different points in time), you wouldn’t be able to implement that with a simple transition.
So basically, you’re right that an animation isn’t necessary for doing something as simple as this. But there definitely are cases where it would be necessary. Does that make sense?