In its most basic form, character animation is about storytelling. As you will see, characters drive a story, and, in turn, the story further defines the character. A good story gives characters motivation, conflict, and a path of action. Without these things, your characters will not truly spring to life.
Developing a Story
Story structure has a few important concepts. First, you need a character who is motivated by a need. To achieve that need, the character must overcome obstacles. As the character deals with the obstacles, the audience learns more about who the character is. It is simple to explain, but telling a good story is an art form in itself. Now that you understand some of the basics of storytelling, you can start to develop stories of your own.
What type of story do you create? There are quite a few. There's the simple story with a full plot that has a beginning, middle, and end. There are also stories that are really just a collection of gags strung together, as in a Road Runner cartoon. Even those simple cartoons have the essential basics of a story: The Coyote's motivation is to catch the Road Runner. He just seems to encounter plenty of obstacles along the way.