Express notice is when information is actually delivered to a party. This is different from a letter or an email being sent. Express notice means that the person in question has definitely received the information. Express notice is important in issues regarding liability. The reason is because a party who receives express notice can then be held accountable for the information if they are required to by law.
Express notice is basically the successful delivery of a message to a person. For example, if a power line goes down in front of a person's house, and they call the power company and informs them of the incident, then the power company received express notice. The power company may then have a legal obligation to come and fix the downed power line before someone gets injured by accidentally touching it. Otherwise, they could potentially be held liable for the damages.