Liebeck was hospitalized for 8 days with multiple skin grafts. She asked asked McDonalds for medical expenses from the injury from the coffee and lost wages (<20k). McDonalds offered $800.
At that point she got an attorney. They tried to settle. McDonalds refused. In the trial it came out that McDonalds had more than 700 reports of medical injuries from the coffee that they were aware of. Their internal quality control manager reported that they recognized that they were posing a burn hazard to customers with the heat of their coffee, but that it was a minor concern that they were unwilling to adjust.
McDonalds admitted that not only were they burning customers who drank the coffee straight from the cup, many of whom needed medical treatment, but that this was something they were unwilling to change.
That's why the jury hit McDonalds with punitive damages of the profits of two day's sales of coffee (which the judge reduced). Through the whole process McDonalds was acting like a criminally negligent bully unconcerned with injuring customers. Punitive damages did correct this.