As your tag implies, Hedley Bull was a member of the English School of international relations. This school of thought is a constructivist school of thought that does not completely reject realism but which criticizes that school of thought. This is what Bull is trying to say in this chapter -- he is trying to say that there is such a thing as an international society and that states do not exist merely in a Hobbesian state of anarchy.
Bull points out that there has long been some degree of cooperation between states. The actions of states have also long been regulated by a set of standards that all states have been expected to abide by. This is not to say that states always play by the rules or that they always cooperate. However, Bull is arguing that the realists are missing something when they argue that the international system is characterized only by anarchy.
So the major point of this chapter is that anarchy is not the only characteristic of the international system. Instead, states show a strong tendency to cooperate with one another and to abide by unwritten "laws" that help to constrain their actions. Both of these ideas are contrary to what realists believe should be the case.