What are the main points in Raymond Williams' "Dominant, Residual, And Emergent"?
It's a bit ironic to ask the main points of "Dominant, Residual, And Emergent" in Marxism in Literature, since the title of the selection speaks so much for itself! However, ... I would say (in expansion) that the main points are explaining dominant ideology, residual ideology, and emergent ideology.
The book itself has much more than this one selection, including lots of contributors to Marxist theory (in addition to Marx) such as Lukacs, Althusser, and Goldmann. Further, Williams adds his own name to the list by adding a new theory: "cultural materialism" which adds Marxist theory to literature. Before he gets to the ideologies you ask about, he discusses things like determinism and hegemony in literature at length.
But to get to the meat of your question, these three ideologies you mention must be defined. First, a dominant ideology has to be espoused by most of society. That is why it's dominant. Even within a dominant ideology, though, residual ideologies usually exist. A residual ideology is one that WAS dominant in a previous time period. (Residual ideologies, then, are often the current dominant ones that have been adapted to suit the current culture.) Finally, there are emergent ideologies which are completely new and in direct opposition with the dominant ideology. It is this "fight" between the dominant and the emerging ideologies that makes change happen.
Thus, put into the context of Marxism in Literature the selection entitled "Dominant, Residual, And Emergent" is most instructive in understanding ideology.
These concepts, explicitly elaborated in Marxism and Literature (1977), contributed to innovate Marxist criticism which had been largely based until then on the analyses of historical epochs according to the prevailing mode of production. While Williams generally agreed with the division of historical periods following this method, he also found them to be too broad and felt the need to make more explicit the conflicts and resistances that occurred within these larger historical formations. Thus, dominant ideologies are those held by the majority of society. They include also residual elements of ideologies that were dominant in the past but that have been replaced. These reisdual elements are re-invented to a certain extent and adapted to the new dominant values. Finally, emergent elements are those which, consciously or unconsciously, set themselves in opposition to the dominant. The social interaction and clash between the dominant and the emergent leads to social change. Eventually emergent elements may become dominant, but this process is not inevitable for all emergent elements, some of which remains confined in the margins of society.