Someone who's disobedient doesn't follow the rules. If your dog won't sit, stay, or heel, you can describe her as disobedient.
When you refuse to obey someone in authority, you're disobedient. A frustrated substitute teacher might describe the entire second grade class as disobedient, and you may try to train your cat to use the toilet but find her to be a disobedient pet. The word comes from combining obedient — with its root of oboedientem, Latin for "obey," — with the prefix dis, or "do the opposite of."