Worldhood has two aspects. (1) The referential totality is the holistic aspect of worldhood. The whole is the gathering of referentiality in the web of relations. World shows up through discovery. (2) The involvemental whole grounded in virtue of somebody taking a stance and realizing their role along with the role of the gear with which they deal. The world shows up in disclosure.
The veiled/revealed or withdrawn/obtruse or internal/external motif is Heidegger's fundamental truth. He is forever interested in the innie and outie aspect of the world's navel. He is drawn to that flicker that is evinced in the depression and spring of pressing buttons. The press of the the button is its involvement as gear. What does it mean to let the y key of the keyboard or any gear be involved in-the-world?
Letting gear be is letting it unfold as gear. Letting gear be is letting gear take its turn and play its role. Letting gear be "means rather that something which is already an 'entity' must be discovered in its readiness-to-hand, and that we must thus let the entity which has this being be encountered. This 'a priori ' letting-something-be-involved is the condition for the possibility of encountering anything ready-to-hand" (BT, p. 117).
We're working our way down a dark path here. We must differentiate the internal and external structure of world without reducing it beyond perception. As always with this kind of thinking, it helps to stick to everyday life. Let's consider our sunglasses again.
What does it mean to let our sunglasses be? What does it mean to discover versus disclose our sunglasses? Letting sunglasses be involved in the ontical sense is discovery. We realize the role that sunglasses may play in-the-world. This has to do with the as structure. We can think of it as how sunglasses are used to play a role. "When we let something be involved, it must be involved in something; and in terms of this "in-which", the "with-witch" of this involvement is freed" (BT, p. 117-118). This means that letting our sunglasses be involved happens based on the condition of the possibility of there being a glinted upon eyeball and a shiny thing in general. What gets freed in that possibility space is the action of the sunglasses to be dealt with and for the sunglasses to play their role in dealing with the shining thing. The sunglasses are discovered through our concern for the sun rays and we deploy the glasses in their played role based on a familiarity. We deal with the glint. Entities get discovered as the not me distinguished from a somebody. Heidegger differentiates the quality of discovery, "discoveredness" as a quality of non-Dasein. In making the posthuman turn, I claim (with Harman and the OOO crew) that discovery has to do with one object (body, matter, thing, notion) dealing with another without regard to the status of the entities.
Now consider disclosure. Disclosure is ontologically prior to discovery. With the blue cube above, the inner cube is disclosing the outer while the outer discovers the inner. Disclosure and discovery are synchronic. They happens as an unfolding event. For the sake of terminology, this differs from an occurrence. Events happen and unfold. Events take place. Occurrences are particular instants. Occurrences are incidents. Just as events are the condition of the possibility of incidents, disclosure is the condition of the possibility of discovery, as well as familiarity is the condition of the possibility of concern.
"The previous disclosure of that for which what we encounter within-the-world is subsequently freed, amounts to nothing else than understanding the world--that world towards which Dasein [somebody] as an entity always comports itself" (BT, p. 118). Disclosure is akin to understanding. Discovery happens when somebody explicitly considers the roles. It is an active realization of the referential whole. Disclosure is implicit. With the sunglasses, disclosure is not so much the dealing with an entity as much as it is the being dealt with of ourselves. In the case of disclosure, sunglasses are not used to shade somebody from the sun. With disclosure, somebody is used to sunglasses. The sunglass gear is understood. Instead of "dealing with it", somebody "get's used to it". Somebody does not deal with sunglasses with disclosure. Rather, they allow for the possibility space for the sunglasses to "do their thing". This means that somebody grants the sunglasses clearance "to sunglass".
When we discover our sunglasses we are dealing with the entities in-the-world as entities playing their roles. When we disclose the sunglasses we are dealing with our own existence. We are dealing with the condition of having been already dealt in-the-world. Disclosure is an act of understanding in the sense that with our cubes, the internal cube stands under and within the world of the outside cube. Discovery is outstanding or thinking of things outside yourself. Discovery takes the view from nowhere. Disclosure happens in place.
With these notions, discovery and disclosure, we draw closer to worldhood. What makes up worldhood is the assignment of somebody in-a-world to a role in-the-world. "The "wherein" of an act of understanding which assigns or refers itself, is that for which one lets entities be encountered in the kind of being that belongs to involvements; and this "wherein" is the phenomenon of world . And the structure of that to which Dasein assigns itself is what makes up the worldhood of the world" (BT, p. 119).
Worldhood is the structure of an act like creating a map that simultaneously keeps track of the mapmakers position. Look at the cubes again. The mapmaker is first inside the outer cube then outside the inner cube and forevermore being-in-the-world. The interplay of the cubes is worldhood.