I'm not an attorney but as I understand the idea of willful infringement it is that the infringer had notice (knew of the existance) of the patents, were aware that the patents covered their product and kept on infringing after that notice.
A similar sort of legal action can take place where a person who knew or should have known that something they were doing was dangerous (like driving without brakes) and then injure somebody because of their negligence. Not only will they have to pay damages for the loss that they cause, they will also have to pay an extra amount (or possibly even go to jail) as a punishment for the negligence.
The bottom line here is that if you manage a company and receive a notice of infringement from a patent owner you should take it seriously and let the company legal people deal with it. Many company managers/owners just throw those notice letters in the trash but it will likely come back to haunt them.