When motion is overused, it can become a distraction. When used correctly, animation can draw attention to areas where you want to make the most impact.
In the above example from Real Thread, you're greeted with a simple page load animation that introduces the brand (in the navigation), drops the main heading into the frame (telling what they do), then finishes with the calls-to-action fading in.
Nothing is ever really still in the world around us. Experiences with subtle movements feel natural, creating a much more interesting experience that just feels right.
But don't go overboard. Uncoordinated motion from all directions can overwhelm visitors. The ideal experience would resemble a peaceful walk in the park rather than a jog through Times Square.