To understand what is meant by "da-sein" we should look at direct translations into English before trying to distinguish this term as something different. In English this basically means "being there", "presence", or more usually, "existence".
In Being and Time Heidegger is concerned from the outset with the concept of "being".
The first definition of "dasein" by Heidegger is presented and I will try and do it justice by typing out a large segment that contains a little of the context, if not the previous few paragraphs that look at the "question" in general (the "question" is expressed well enough in the following quote though - although I feel it would've been mor ehelpful to frame his explanation by using the term "proposition" rather than "presupposed" ... see full text for that p.5-6. Although the reason for this avoidance becomes clearer later on in his reconstruction):
He goes on to explain why it is not circular reasoning and examines the difference between "presupposing" and "propositions". This does little more than reveal the age old problem of the "question" philosophy still has no way of dealing with. To skip to half-way through the next paragraph Heidegger says:... Everything we talk about, mean, and are related to is in being in one way or another. What and how we ourselves are is also in being. Being is found in thatness and whatness, reality, the objective presence of things [Vorhandenheit], subsistence, validity, existence, and in the "there is" [es gibt]. In which being is the meaning of being to be found; from which being is the disclosure of being to get its start? Is the starting point arbitrary, or does a certain being have priority in the elaboration of the question of being? Which is the exemplary being and in what sense does it have priority?
If the question of being is to be explicitly formulated and brought to complete clarity concerning itself, then the elaboration of this question requires, in accord with what has been elucidated up to now, explication of the ways of regarding being and of understanding and conceptually grasping its meaning, preparation of the possibility of the right choice of the exemplary being, and elaboration of the genuine mode of access to this being. Regarding, understanding and grasping, choosing, and gaining access to, are constitutive attitudes of inquiry and are thus themselves modes of being of a particular being, of the being we inquirers ourselves in each case are. Thus to work out the question of being means to make a being - one who questions - transparent in its being. Asking this question, as a mode of being of a being, is itself essentially determined by what is asked about in it - being. This being which we ourselves in each case are and which includes inquiry among possibilities of its being we formulate terminologically as Da-sein. The explicit and lucid formulation of the question of the meaning of being requires a prior suitable explication of a being (Da-sein) with regard to its being.
So what is "Da-sein"? How is it differing from the term "self"?... "Presupposing" being has the character of taking a preliminary look at being in such a way that on the basis of this look beings are already given are tentatively articulated in their being. This guiding look at being grows out of the average understanding of being in which we are always already involved and which ultimately belongs to the essential constitution of Da-sein itself. Such "presupposing" has nothing to do with positing a principle from which a series of propositions is deduced. A "circle of reasoning" cannot possibly lie in the formulation of the question of the meaning of being, because in answering this question it is not a matter of grounding by deduction but rather laying bare and exhibiting the ground.
I actually find the above quotes easy enough to grasp, but I still find them needlessly obtuse. Later on Heidegger appears to merely create his own little language game, which may be useful to some. My issue is that it is a "language game", and that he should've said the "game" is "dasein" perhaps?
The main issue for me is Heidegger's failure to distinguish between the concept of "self" and "dasein". To me it looks a lot like a looking at oneself "as if" oneself is "other". In this way I do very much find Heidegger's work here useful in exploring this area for the numerous traps laid before us in attempting to view "this" or "that" as purely "subjective" or purely "objective", both being essentially the same thing wrap around itself - so to speak! So I understand the difficulty presented by language in explicating an all too (very much TOO TOO) obvious "being".
-- Updated July 28th, 2017, 1:41 am to add the following --
A further, and perhaps more clear, exposition of Da-sein is shown here (p.13-14):
I would again argue strongly that this is needlessly obtuse. What the reader should understand here is Heidegger is basically asking what it is we found questions on and from "where" these founding arise. It is a bold attempt to create a concept parallel to language for lingual usage (an attempt that has to fail necessarily).... Only when philosophical research and inquiry themselves are grasped in an existentiall way -as a possibility of being of each existing Da-sein - does it become possible at all to disclose the existentiality of existence and therewith to get hold of a sufficient grounded set of ontological problems. But with this the ontic priority of the question of being has also become clear.
To put this into simpler terms, he is talking about PRIORITY in the last line. He is removing the idea of "proposition" and talking about the "prior" to the "proposition" - the "proposition" being understood by Heidegger as being presented after-the-matter-of-factly, a deduction revealed as being nothing other than inference, or induction!
Instead he implants the rehashed concept of "presupposed".
To step away from this confusing rhetoric we can simply regard ourselves and our understanding of self. I am. I am neither "here" nor "there", the "hereness" and "thereness" is, for me, a way of registering The World (My World "seen" as I "see" not as it "sees" me). The World has "being" only in regard to my understanding of my own being which remains both paradoxically hidden and exposed ... what Heidegger is really attempting to frame here is this concept of the "non-whatness" of the equally "hidden"/"exposed" item and call it Da-sein (in common English "being-there" or "existence").
HE seems to mistaken the "horizon" as "being" over-there in the way he expresses his definition of "dasein". Later in Being and Time, I cannot remember exactly, I do think he ignores this entirely and acts as if the concept of dasein doesn't suffer when he talks about "horizons" (this could be due to my personal take on "horizon" though! Hopefully you'll help reveal this if you're more familiar with Heidegger than I am).
