Oceans of ink have been spilled over the centuries on the celebrated distinctio realis between essence (essentia) 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)  We can say first of all that the real distinction is so-called because it is not a merely conceptual or notional or logical distinction.  'Real' from the Latin res connotes something the existence of which is independent of finite minds such as ours. So the real distinction 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 when we view them, or how we refer to them or think about them.   The terms 'MS' and 'ES' express two different "modes of presentation" (Darstellungsweisen in Gottlob Frege's terminology) of one and the same massive chunk of extra-mental physical reality, the planet Venus.  So one might think that the real distinction between essentia and esse is like the distinction between Venus and Mars. Venus and Mars are not abstract modes of presentation but concrete entities in their own right.  Venus and Mars are distinct in concrete reality, not merely in conception, or distinct at the level of Fregean Sinn (sense).

2) But although the Venus-Mars distinction is a real distinction, the distinction between essence and existence cannot be like it.  For while each of the planets can exist without the other, essence and existence cannot each exist without the other in one and the same thing.  A thing's existence is nothing without 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 from which I am now drinking would be nothing without the cup and thus without the cup's total or 'wide' essence.

3) A tripartite distinction has emerged: thing, existence of the thing, essence of the thing. A sentence ago I used the phrase 'wide essence.' Why?  Because 'essence' (quiddity, whatness) can be taken in two ways, one 'wide' the other 'narrow.' The wide essence encompasses all of a thing's quidditative determinations (Bestimmungen). We can think of wide essence as the conjunction of all of a thing's quidditative attributes. Socrates and Plato, for example, differ in their wide essences despite the fact that they are both essentially human and essentially rational, and univocally so, to mention just two of their essential, as opposed to accidental, attributes. For the one man is sunburned, let us say, while other is not.   So while they differ in their wide essences, they do not differ in their narrow essence: the two share their essential properties, being human, and being rational, and others as well.

4)  I said that it is obvious that the existence of a concrete individual  would be nothing at all apart from the wide essence of that very same concrete individual. How could the existence of Socrates, that very man, be anything at all apart from the ensemble of his attributes? The existence of a thing is not like the pit of an avocado that can be removed from the avocado and exist on its own.

It is rather less obvious, if at all obvious, that the wide essence of a concrete individual would be nothing without existence.  Why couldn't there be a wholly determinate individual essence that does not exist? Why couldn't it have been that before Socrates began to exist he was a wholly determinate individual essence?    His coming to exist would then be  the actualization of a pre-existent wholly determinate merely possible individual essence. On such a scheme when God creates, he does not create ex nihilo, out of nothing, but out of mere possibles.  He creates by conferring existence (actuality) upon  wholly determinate  individual essences which before their creation are merely possible items.

If, however, as Thomas maintains, creation is creatio ex nihilo, then the essence and the existence of a concrete individual are each nothing without the other. Here we take the Thomist line.

5) The essence and the existence of a particular individual are thus each dependent on the other but nonetheless really, not merely notionally or conceptually, distinct.  They are 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 a good analogy might be the convexity and concavity of one of the lenses.  The convex surface of a particular lens cannot be without the concave surface of that very lens 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. The distinction is not a matter of our projection, or imposition, or interpretation.  There is a real mind-independent difference.  But it is only  an analogy. If the distinctio realis is an essential structural determination of finite beings, it is presumably sui generis and only analogous to the distinction between convexity and concavity in a lens.

6) Now what reason could we have for accepting something like the real distinction?  Here is one of Geach's arguments, based on Thomas 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.  In keeping with my distinction between the rationally acceptable and the rationally compelling,  I find the argument rationally acceptable, and I incline to accept it.  Unfortunately many others, including many distinguished Thomists, do not. And that fact gives me pause, as it must, given my commitment to intellectual honesty. (More fuel for my aporetic fire.)

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. For illustration we turn to Max Black.

Max Black was famous for his iron spheres.  (Geach does not mention Black.) In a well-known article from way back, Black 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, and in every other relational and non-relational feature, there is a real distinction between existence and essence in each sphere.

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.