You generalize and form a rule that takes into account the facts of the case by making an inference from the holding of the case. Two dogs were fighting, and a man tries to separate the dogs with a stick. He is seriously hurt in the process and sues the owner of the dogs for negligence. Thus the owner of the dogs is not liable. You can infer several principles from that holding.
Most students just copy the rule from the casebook verbatim into their notes.
The more astute student restates the rule in her own words in order to get a clearer sense of what has to be proven in order to apply the rule. Stating the rule is a two-part process. As with any course of study or in any form of communication, when you restate what someone else has said in your own words, you are making sure that you understand the nuances of everything they have said. In a way, you are creating your own mini-Restatement of the law in the words of a 21st century lawyer. You can then compare what you have said with the case law to see whether you have understood all of the elements correctly.