That is the title of a 1959 book by the sociologist C Wright Mills. As the wiki will tell you, it's common for intro Sociology classes to use that phrase to introduce sociology and try to explain what it is and why anyone should care about it. That seems like a good place to start to me as well, although I don't intend to actually reference that particular text very much.

Here's a good summary from a professor at Cornell:

It's a good place to start because a lot of what makes social sciences contentious, IMO, is in the way they tend to challenge common beliefs about the relationship between supposed dichotomies of "nature" and "nurture", (social) "structure" and (individual) "agency" (see the link above), Individualism and Collectivism (as political philosophies), and so on. So, to start from the very beginning, I would argue that the importance of "the sociological imagination" comes first of all from the fact that human beings are social beings, and that our sociality is intrinsic to our nature. Therefore, any deep understanding of human behavior must account for those social qualities, and overly reductionistic accounts of human behavior which try to subordinate the social with the individual are very likely to fail.

Here are a few of my favorite social scientists:

-- Clifford Geertz, "The Impact of the Concept of Culture on the Concept of Man" (The Interpretation of Cultures, 1973, pp. 34-6)

-- Berger and Luckmann, The Social Construction of Reality (1966, p. 51)

Berger and Luckmann might seem to overstate things a little when they write that "none of these formations may be understood as products of man's biological constitution", but bear in mind they don't mean there is no relation whatsoever between human biology and behavior, they just mean that the latter cannot be reduced to the former, nor can the collectivity of human behavior be reduced to a simple aggregation of individual psychology.

For a more modern empirical take on the intrinsically social nature of distinctive human being, see for example Becoming Human: A Theory of Ontogeny.

What "The sociological imagination" first aims to do then, is to make clear the importance of understanding sociality to understanding humanity. Berger and Luckmann go on to develop a theory of the sociology of knowledge (how is human knowledge produced?) which elaborates in a general way on what this means, which I'll briefly outline next.

In The Social Construction of Reality, Berger and Luckmann conceptualize the "production of a human environment" mentioned above as process in which three "moments" interact with each other in an on-going way (they use the technical term dialectic, but we can ignore that).

Those moments are externalization, objectification, and internalization. They write about knowledge, but I think this conceptual framework is a useful general way to think about the relationship between the individual and culture.

Externalization means, very simply, that we create things through our being. Physical artifacts, but also ideas, language, art, and so on. We're always going on producing things. But the things which we produce do not remain confined to our individual minds -- not even the ideas. Through social interactions they come to have a kind of objective (or at least intersubjective) existence. This becomes especially clear over the course of generations, because for the young the collective knowledge and beliefs of parents are understood explicitly in an "objective" way (cf. Becoming Human on this point). But, that is not the end of the story, because those "out there" ideas are also internalized by us, and in the process modified, re-externalized in our new beliefs and behavior, re-objectified, and so on.

Berger and Luckmann analyze the process of objectification with the help of a few different concepts. The first is Habitualization, which provides a means of understanding the sociological concept of an "institution":

The book, of course, goes into more detail, but I think the simple concept is hopefully evocative enough. The point is that the habitualization of activities and specifically the knowledge associated with those habits ("how to plant a garden"; "how to fix a flat tire"; ...) is a human product, and in the process of sharing that knowledge with others it comes to take on a more concrete existence, such that when young children acquire knowledge of this sort they not only understand it as "this is one way to do this" but as "this is how one ought to do this" (cf. Becoming Human). We have evolved this tendency to institutionalize knowledge and give it a normative dimension because it facilitates social cohesion.

As Berger and Luckmann mention, it's not just patterns of action which become habitualized and then institutionalized, but also expectations that certain types of individuals are the ones who properly perform those same actions. This is the sociological concept of a Role. Think for example of gendered expectations in many societies about which types of activities are suitable for men and women. It may be a man's role to change the flat tire and a woman's role to cook dinner, at least in some cultures. These sorts of stereotypical expectations become externalized and objectified just as the knowledge of how to do those tasks is institutionalized. This applies to almost every aspect of human social existence.

In relation to the sociological imagination then, the point here is that if you want to understand how a person acts, what she thinks, and so on it will be necessary to understand how institutions and roles are constructed within her culture ("structure"), and not just her individual beliefs and preferences ("agency'). This is because our individual beliefs and actions are clearly shaped by these external structures, even in very mundane ways, and we attach significance and meaning to those roles and patterns of behavior that go far beyond simply understanding them as "one way out of many". We internalize socially produced knowledge.

Understanding the meaning we attach to behavior leads then to the concept of Legitimation, which is important in Berger and Luckmann's account.

One potential limitation of focusing on the development of institutions, roles, norms, beliefs and so on via a process that flows in one direction, from externalization to objectification, is that it will lead to a very static picture of culture or social organization. But clearly all these things are in constant flux. In this theory, that is accounted for by the feedback loop between internalization and (re)-externalization. We are also always engaged in processes of renegotiating all of these things: knowledge, roles, institutions, and so on. But there is clearly an interesting kind of stability here as well. We don't instantly abandon all of the beliefs of our parents.

Legitimation, then, describes the processes by which existing social structures are defended. Alongside the production of the knowledge

1) "how to do X"

and the belief that

2) "role Y should do X",

a very similar process leads to the production of explanations for

3) why is it right that X should be done this way by Y?

Those explanations are "legitimations". Berger made great use of this framework for investigating religious legitimations in particular, which tend to try to make such explanations metaphysically absolute: "It is right to do X because [God wills it] or [it is according to our fundamental nature]" and so on.

My hope is that thinking about these very general theoretical considerations will help make clearer the value of "the sociological imagination" to understanding human existence, and why "structural" approaches to understanding human behavior have something to contribute beyond approaches which interrogate individual psychology in isolation.