you grasp the facts and the principles involved, and which also is an aid to class discussion.  Generally, what I recall from law school is this pattern:

Case caption - Provide the name of the case and its legal citations for example, Terry v. Ohio, 393 US. 1(1968)

Facts of the case - These should be very briefly stated, no more than one paragraph, and sometimes only a few sentences.

Procedural History - Explain how the case went from the trial court to the appellate courts that followed, who won and who lost at each level, who appealled.

Issues involved - What legal issue was involved on appeal?

Holding - What decision did the court make?

Rationale - Upon what did the court base its decision?

Disposition - Where does the holding leave the parties? For example, some cases are not done after the court makes a ruling because the case is remanded (sent back) to the trial court.

Concurring and dissenting opinions - Sometimes not everyone on the court agrees, which results in a dissenting opinion you are expected to briefly summarize.  In other cases, there is agreement among the judges about the holding, but a judge or two (or three) will have a different reason for that decision and write an opinion explaining his or her point of view.  This, too, should be summarized very briefly.

When I was in law school, we were expected to brief a case using only sheet of legal pad paper, sometimes for decisions that were more than sixty pages long. It is a challenge, but it can be done.

When I went looking to see if anything had changed, I found a link that I have provided below, which is exactly the way I briefed cases in law school.  Once you get accustomed to this form, you will find it incredibly useful to grasp the essence of a case and to be able to discuss it intelligently in class.