Oceans of ink have been spilled over the centuries on the celebrated distinctio realis between essence and existence (esse). You have no idea how much ink, and vitriol too, has flooded the scholastic backwaters and sometimes spilled over into mainstream precincts. Anyway, the distinction has long fascinated me and I hold to some version of it. I will first give a rough explanation of the distinction and then examine one of Peter Geach's arguments for it.
1. First of all, we can say that the real distinction is so-called because it is not a merely conceptual or notional distinction. It is not like the distinction between the Morning Star and the Evening Star. It is not a distinction parasitic upon how we view things or refer to them. It is more like the distinction between Venus and Mars. The MS and the ES are two "modes of presentation" (Fregean Darstellungsweisen) of one and the same chunk of extramental physical reality, the planet Venus. But Venus and Mars are not modes of presentation but entities in their own right. Venus and Mars are distinct in reality not merely in conception.
2. But although the Venus-Mars distinction is a real distinction, the distinction between essence and existence cannot be like this. For while each of the planets can exist without the other, essence and existence cannot each exist without the other. A thing's existence is nothing wthout the thing whose existence it is, and thus nothing without the thing's essence. I hope it is obvious that the existence of this particular coffee cup would be nothing without the cup and the cup's individual essence.
3. It is less obvious that the individual essence would be nothing without existence. But to make the problem more difficult I will assume that there are no nonexistent individuals, that nothing is an individual unless it exists. This implies that before Socrates came into existence there was no individual essence Socrateity. His coming into being was not the actualization of a pre-existent wholly determinate individual essence. (This has implications for the theory of creation: it imples that creation is out of nothing, not out of mere possibles.) It also implies that there is no individual essence corresponding to the name 'Vulcan' when this is used to denote an intra-Mercurial planet. My assumption is anti-Meinongian and (I believe) also anti-Avicennian. (There was a time, long ago, when the Muslims weren't total slouches when it came to philosophy. 'Avicenna' is the Latinization of 'Ibn Sina.')
4. The essence and the existence of a particular individual are thus each dependent on the other but nonetheless really, not merely notionally, distinct. Really distinct (like Venus and Mars, but unlike the Morning Star and the Evening Star) but inseparable (unlike Venus and Mars). They are really distinct like my eye glasses and my head but not separable in the manner of glasses and head. So an analogy mght be the convexity and concavity of one of the lenses. The convex surface cannot be without the concave surafce and vice versa, but they are really distinct. 'Convex' and 'concave' are not merely two different ways of referring to the same piece of glass. There is a real mind-independent difference. But it is only an analogy.
5. Now what reason could we have for accepting something like the the real distinction? Here is one of Geach's arguments, based on Aquinas, from "Form and Existence," reprinted in Peter Geach, God and the Soul (Thoemmes Press, 1994), pp. 42-64. Geach's argument is on p. 61. I'll put the argument in my own way. I find the argument convincing.
Suppose you have two numerically distinct instances of F-ness. They don't differ in point of F-ness, since each is an instance of F-ness. But they are numerically distinct. So some other factor must be brought in to account for the difference. That factor is existence. They differ in their very existence. Since they differ in existence and yet agree in essence, essence and existence are really distinct.
Max Black was famous for his iron spheres. (Geach does not mention Black.) He hypothesizes a world consisting of just two of them and nothing else, the spheres being alike in every relational and monadic respect. In Black's boring world, then, there are two numerically distinct instances of iron sphere. Since both exist, and since they differ solo numero, I conclude that they differ in their very existence. Since they differ in their existence, but agree in their iron sphericity, there is a real distinction between existence and nature or essence.
Suppose you deny that. Suppose you say that the spheres do not differ in their very existence and that they share existence. The consequence, should one cease to exist, would be that the other would cease to exist as well, which is absurd.