Dasein always understands itself in terms of its existence—in terms of a possibility of itself: to be itself or not itself. Dasein has either chosen these possibilities itself, or got itself into them, or grown up in them already. Only the particular Dasein decides its existence, whether it does so by taking hold or by neglecting. The question of existence never gets straightened out except through existing itself. The understanding of oneself which leads along this way we call "existentiell".1 The question of existence is one of Dasein's ontical 'affairs'. This does not require that the ontological structure of existence should be theoretically transparent. The question about that structure aims at the analysis [Auseinanderlegung] of what constitutes existence. The context [Zusammenhang] of such structures we call "existentiality". Its analytic has the character of an understanding which is not existentiell, but rather existential. The task of an existential analytic of Dasein has been delineated in advance, as regards both its  possibility and its necessity, in Dasein's ontical constitution.
So far as existence is the determining character of Dasein, the ontological analytic of this entity always requires that existentiality be considered beforehand. By "existentiality" we understand the state of Being that is constitutive for those entities that exist. But in the idea of such a constitutive state of Being, the idea of Being is already included. And thus even the possibility of carrying through the analytic of Dasein depends on working out beforehand the question about the meaning of Being in general.
Sciences are ways of Being in which Dasein comports itself towards entities which it need not be itself. But to Dasein, Being in a world is something that belongs essentially. Thus Dasein's understanding of Being pertains with equal primordiality both to an understanding of something like a 'world', and to the understanding of the Being of those entities which become accessible within the world.2 So whenever an ontology takes for its theme entities whose character of Being is other than that of Dasein, it has its own foundation and motivation in Dasein's own ontical structure, in which a pre-ontological understanding of Being is comprised as a definite characteristic.
1 We shall translate 'existenziell' by 'existentiell', and 'existenzial' by 'existential' There seems to be little reason for resorting to the more elaborate neologisms proposed by other writers.
2 '... innerhalb der Welt ...' Heidegger uses at least three expressions which might be translated as 'in the world': 'innerhalb der Welt', 'in der Welt', and the adjective (or adverb) 'innerweltlich'. We shall translate these respectively by 'within the world', 'in the world', and 'within-the-world'.