When you describe a person as "animated", it means that they:
- seem excited
- move around a lot
- make hand gestures
- move their face around a lot
You usually use "animated" to describe the way that someone speaks or tells a story.
You might be more familiar with the word "animated" as it's related to cartoons. An "animated" movie or video is made using drawings or 3D images that move around. The basic meaning of the word "animate" is "to make something seem alive", so that's where the two meanings of "animated" come from.