What we need to understand, which I have mentioned in the answers to other questions is that Being is a wholly Indo-european linguistic phenomena. And that the contrast between Being and Existence is a historical confrontation between languages which have and do not have Being, in particular Arabic and Greek. As the Arabs learned Greek philosophy they eventually realized this difference between ontos (being) in Greek and wajud (found) in Arabic. So the Arabic Philosophers created a term Kun (make) to represent what was in Being that was not covered by Existence, the surplus, the supplement as Derrida would say. Then when the Arab philosopher’s works were translated back into Latin there was no word in latin for wajud (found, ecstasy) and so the Latin translators of the Arabic philosophy texts made up a technical term for what the Arabs called “wajud” which was “Existence” which was given the same range of manings as wajud. Within the Western tradition this term had little relevance until it was taken up as an alternative to Being by the Existentialists. For most of the tradition Essence preceded Existence, but the Existentialists especially Sartre reversed that to say that Existence precedes Essence, which is obviously true, because only Indo-europeans have that linguistic construct. However, the fact that the Existentialists were using “Existence” did not mean they had escaped Being, but in fact they merely used the term to describe for the most part the becoming nature of Being. This fact that “Existentialists” did not escape from Being in their formulation of the meaning of “existence” is fateful for us and our tradition. In other words when we looked into the mirror of the Other of “existence” we merely saw a reflection of Being, and not existence itself. However, the whole tradition from its mythological roots is oriented toward existence in a fundamental way because, when ever we interacted with the Other we encountered other non-indoeuropean speakers over which we had to assert the superiority of Being over Existence. How each philosopher of Existence represented it is slightly different and thus we need to study the Existentialists to understand how they conceived of this alternative of Being, this anti-being. For instance Sartre called it Nothingness. Heidegger called it the ecstasy of dasein, which projects both Pure (static, present-at-hand) and Process (dynamic, ready-to-hand) Being. Existence is always represented as a Monster over which Being triumphs for instance in the image of St. George and the Dragon (Zeus/Apollo over Typhoon/Python). The defeat of Existence is the prerequisite for the setting up of the regime of the dominance Being, which underwrites the legitimacy of Indo-european domination via expansionism and colonialization. In prehistory this was carried out on the basis of the domestication of the horse which was the basis of indoeuropean expansion thorough the known world, and later it was seen in Western colonialization. This expansioinism is always based on technological superiority. So there is a problematic that Heidegger recognized of the relation between Being and Technology and Nihilism at the root of the Western worldview. He says the essence of Technology is not technological, but instead nihilistic. So the question becomes what is the relation between Indo-european Being as grounding technological innovation, and what is the relation of the dominance that this produces over Existence that shows up as Nihilism?
Since Parmenides thought and Being have been understood as the same. Thus Being means intelligibility within our tradition as a whole. Thus Heidegger says the key question concerns the meaning of Being. In nihilism there is a loss of meaning when we realize that extreme artificial nihilistic opposites (cf Stanley Rosen) are really the identical. Thus there is in the ecstasy of Dasein a projection of being-in-the-world, which produces the horizon of the world that Dasein finds him/her self in. Within that world there are two modalities which are static and dynamic that make up the monolith of Being (cf M. Henry’s critique of Heidegger’s Ontological Monism in The Essence of Manifestation). One of those modes is the ready-to-hand which underlies the circumspective concern with the whole of the technological infrastructure that underlies the presentation of static tableaus of beings within Being. This modality makes possible the production of technological wholes that are emergent and novel that lead to dominance within the world. But the dominance means that Being as a monolith suppresses the natural varieties of languages (based on existence) of the radical Other. This surpression of variety within the world leads to a monism which generates nihilistic opposites within itself due to its radical dualism, and this supplants the natural variety of other standings in the world from other cultures, and worldviews, and languages. When nihilistic opposites annihilate, cancel, or contradict each other then that produces nihilism within the Western worldview itself, so despite dominance there is a sapping of meaning within the Western worldview as a fundamental syndrome or miasma within our culture. This is called the intensification of nihilism.
So you can see that when you ask What does it mean for something to exist? you have opened up a can of worms. In our tradition meaning is seen as intrinsic to Being and Existence is seen as meaningless, or at least the babble of the BarBarian. However, seeing the other as meaningless, recoils on us until we recognize our own chatter within the plenum of Being which has achieved dominance by suppressing all other standings toward the world. Essentially, traditionally we have seen existence as meaningless, and thus asserted a duality between ourselves and the other, but then asserted our dominance over the heterogeneity seen in Existence and thus produced a Monism of Being that due to its extreme dualism ends up in a world that is meaningless as the result of claiming meaning only for itself. Without difference the result is meaninglessness. This is a fundamental bind within the Western worldview that generates nihilism within itself via the suppression of the Other of existence due to technological superiority. There is an unintended consequence of suppressing variety and claiming all meaning for oneself wich is that it saps meaning from oneself, and leads to ones own alienation and anomie. Thus in some sense Existence really is a mirror, and in it we see only distorted images of ourselves as Other.
Seeing meaning in existence is one of the fundamental steps to get out of this vicious cycle that we are trapped within philosophically. So what does it mean for something to exist? If we can see meaning through the veil of the a priori projection of Being, as a surplus, or supplement, or accursed share (Bataille) then we can get out of the illusion (Maya, Mara, Dunya) that covers over existence. Buddhism tries to do this from within the Indo-european existence by thinking it as nondual (Form is emptiness, Emptiness is form). Hegel in his logic sees “nothing” as Buddhist emptiness, not as a non-thing as does Heidegger. For Hegel “being” and “nothing” combine to give the flux of Heraclitus and that by an aufhebung produces the Dasein or determinate being. Dasein is the term for Existence in philosophical German. Meaning coming out of nonduality rather than Being is the way to escape the illusions projected by Being (‘Sat’ Sanskrit). Buddhism is a heresy of the Indo-european worldview because it tries to get back to existence from within Being via the realization of the nonduality of existence as emptiness. But existence looks different once you have been immersed in a worldview with Being. If you have not been immersed in Being previously then the nonduality looks like the Void (WU) of Taoism. Thus these two interpretations of Existence are themselves dual. And the non-nihilistic distinction between them is made by the projection of the singularity of Ultra Being at the meta-level in Being where we transition to existence, i.e. the fifth meta-level. So it turns out that Being as the projection of illusion is necessary to distinguish between the duals of non-duality of Existence (emptiness and void). This is perhaps the best answer to the meaning of existence. In Existence we are aware of natural heterogeneity both within ourselves and in nature. Being tries to steal with all meaning and appropriate it to itself and tries to suppress all meaning that comes from this natural variety by establishing the monism of Being. In Buddhist wisdom (prajna) we attempt to get back to that primordial meaning of existence. We try to get beyond the flaw in existence that illusion of a priori projection represents. If we can do that then we learn the true and real and identical and present meaning of existence which has no surplus or lack, i.e. which is perfectly nondual. See http://nondual.net for more information on the meaning of existence.