Good and useful animations communicate something, they're not there just to be there or to make it "pretty", which is most designers use them. But they can actually communicate intent, action, immediacy and other important things, if they're used sparingly in the right situations, without actually getting in the way.

Probably the most basic animation most of us PC users see every day is the very basic animation of a text cursor blinking on/off in text fields, like the one I write it right now. It's super basic, but communicates that the computer is waiting for you, it's alive and you can enter things. If it was static, you get the impression something is stuck instead, or couldn't tell exactly where the cursor is at a glance. But it blinks, and that tells us stuff.