Heidegger's Terminology and the Everyday

One of the primary difficulties with coming to understand Heidegger's thought is his terminology. Here's an instructive excerpt by Dorothea Frede concerning the methodological reason behind his unorthodox prose:

Since Heidegger disagreed with Husserl's assumption that there is an impersonal ego providing us with incontestable truths, he had to work out who that entity really is that in its very nature has a concern with the question of being [i.e. man]. Because he did not want to foist yet another artificial construction on this entity in his own interpretation, Heidegger started his phenomenological investigation by capturing the phenomenon that all philosophers before him had "passed over" as trivial and not worth the theorist's attention, namely, everyday existence. The vocabulary he introduced to characterize the various features of everyday existence and its structure was designed to avoid all associations with common philosophical terminology; it was not designed to turn it into a secret doctrine only open to the initiate. His terminology, though often unusual in German, is much easier to understand than its English counterpart, because Heidegger plays with easily comprehensible etymological family relationships that often do not exist in English.
"The Question of Being," in The Cambridge Companion to Heidegger, Charles Guignon, ed. (New York: Cambridge University Press, 1993), 54.

Heidegger's concern with the "everyday" is quite transparent in his work: instead of examining scientific taxonomy or worldview construction, he examined such everyday occurrences as opening doors, using hammers, boredom, and jugs/bridges. Rather than turning to the Platonic ideal of abstract thinking that had been recently reemphasized by Descartes' detached self, Heidegger got into the dirt and grime of common activities. And why shouldn't he? We speak of and understand being just as much in eating food or being in our 'own little world' as we do in doing science. This is aptly seen in a story by Aristotle that Heidegger discusses in his "Letter on Humanism" (Miles Groth trans.). Men come to see Heraclitus and are surprised to see him warming himself by his stove. Heidegger comments:

Instead of [finding some spectacular or interesting thing] the sightseers find Heraclitus by a stove. That is surely a common and insignificant place... In this altogether everyday place he betrays the whole poverty of his life. The vision of a shivering thinker offers little of interest. At this disappointing spectacle even the curious lose their desire to come any closer. What are they supposed to do here? Such an everyday and unexciting occurrence--somebody who is chilled warming himself at a stove--anyone can find any time at home. So why look up a thinker? The visitors are on the verge of going away again. Heraclitus reads the frustrated curiosity in their faces. He knows that for the crowd the failure of an expected sensation to materialize is enough to make those who have just arrived leave. He therefore encourages them. He invites them explicitly to come in with the words, Einai gar kei entautha theous, "Here too the gods come to presence."
"Letter on Humanism," Frank A. Capuzzi and J. Glenn Gray, trans., Basic Writings, 257.

It is, in fact, the fixation on the 'higher' world of the sciences and abstract reasoning as the basis for metaphysics that has caused the Western tradition to go astray. By returning to the everyday, to that which is most near to us and is most likely to be passed over (it is so...common), Heidegger allows beings to speak to us as they always already do, not as our ideological desires for scientific or mathematical precision would have them appear. "We would like only, for once, to get to just where we are already" ("Language," in Poetry, Language, Thought, 188). If this requires a new terminology so this new appearing of beings is not immediately pigeonholed into an already-existing philosophy before we allow them to speak, so be it. Such is the danger of letting beings lead our thinking--they just might appear in ways that are not allowed by our preconceptions.