How can I help him understand how serious this is? The teacher is very concerned and has not allowed him to go on the class field trip.
Punishing him is not a healthy response and I am stunned that his teacher did not allow him to go on a class field trip because of his classroom talking. That was neither a logical or a natural consequence to his behavior. She should read The Parent's Handbook for appropriate ways to discipline children.
I would be most concerned that his talking in class might cause him to miss some lessons that might be crucial to his understanding of some academic concepts. I would ask that the teacher(s) consider a seating arrangement that would lead to less socialization and I would ask your son to participate in some discussions with you concerning a plan to solve this problem. He is old enough that he may respond to being the key person to solve his own problem, rather than being punished by you and the teacher and being told to shape up. Encourage his attempts to change -- they may take a while but keep saying you believe in him and really appreciate his efforts. If he can discipline himself, then he can own the accomplishment.