It means that the container will only use the MDB to process one message at a time. Only one thread will be using onMessage(), so the MDB doesn't have to worry about implementing thread-safety protections.
sorry, I haven't got it. The spec 15.4.5 "Serializing MDB methods" says that the container serializes calls to the MDB instances. I don't understand the concept that a method call can be serialized. You can serialise objects and you can call methods, but what does it mean to serialize a method? Or a method call?