Thomas Aquinas, answered from the texts and cited to the page.
God is pure act — actus purus — and to understand what that means one must first understand why potentiality is incompatible with the first being. Whatever passes from potentiality to actuality cannot reduce itself to actuality, for what is merely potential is not yet, and what is not yet cannot act.1 Something prior must bring it from potency to act.
If that something is itself in potency, the same requirement applies, and we cannot go on to infinity. Therefore we must arrive at something that is wholly actual and in no way potential, and this we call God.2 Now consider what follows from the absence of all potentiality. Everything acts according as it is actual; therefore that which is not wholly actual acts not by its whole self but by participation in something.3
The first agent, however, acts by its very essence and not by participation — it cannot be otherwise, for if it acted by part of itself, something in it would remain unrealised, which is to say potential. God therefore has no admixture of potentiality whatsoever.4 From this the identity of essence and existence in God follows necessarily. In any being whose existence differs from its essence, that existence must be caused by another, for nothing can be the sufficient cause of its own existence when that existence is received.5
But God is the first efficient cause, so His existence cannot be caused by another. Therefore His existence does not differ from His essence.6 Put the same point through the act-potency axis: existence is that which makes every form or nature actual — goodness and humanity are spoken of as actual only because they are spoken of as existing. Existence stands to essence as actuality to potentiality.
Since in God there is no potentiality, His essence does not differ from His existence.7 The Compendium presses the same conclusion from a different angle. Since all motion is an issuing forth from potency to act, the ultimate act must be that toward which all motion tends; and since natural motion tends to what is naturally desired, the ultimate act must be that which all things desire.
This is existence itself, ipsum esse. The divine essence, being pure and ultimate act, must therefore be existence itself.8 And because God is not a being that has existence but is existence, He falls under no genus. Species is constituted by specific difference added to genus, so the essence of any species possesses something over and above its genus.
But ipsum esse does not comprise within itself any factor added to some other factor — it is not composed.9 Nor can God be a genus, for what a thing is comes from its genus, but what God is, is very existence itself, and no differences can be apprehended in existence as such, since non-being is not the specific difference of anything.10 What actus purus means, then, is this: a being in which there is no unrealised capacity, no composition of what-it-is and that-it-is, no distinction between essence and existence, no genus and no species — a being that simply is, wholly and without remainder, the act of existing.
it does not reduce itself from potentiality to actuality, because that which is potential is not yet, wherefore neither can it act. Therefore it must be preceded by something else whereby it can be brought from potentiality to actuality.Summa Contra Gentiles Book I, God
we must come to something that is wholly actual and nowise potential. And this we call God.Summa Contra Gentiles Book I, God
Everything acts according as it is actual. Wherefore that which is not wholly actual acts, not by its whole self, but by part of itself.Summa Contra Gentiles Book I, God
the first agent, which is God, has no admixture of potentiality, but is pure act.Summa Contra Gentiles Book I, God
if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused.Summa Theologica Part I, Prima Pars
But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.Summa Theologica Part I, Prima Pars
existence is that which makes every form or nature actual; for goodness and humanity are spoken of as actual, only because they are spoken of as existing. Therefore existence must be compared to essence, if the latter is a distinct reality, as actuality to potentiality. Therefore, since in God there is no potentiality, as shown above, it follows that in Him essence does not differ from existence.Summa Theologica Part I, Prima Pars
since all motion is an issuing forth from potency to act, the ultimate act must be that toward which all motion tends; and since natural motion tends to what is naturally desired, the ultimate act must be that which all desire. This is existence. Consequently the divine essence, which is pure and ultimate act, must be existence itself, *ipsum esse*.Compendium of Theology, pp. 17–18
Species is constituted by specific difference added to genus. Hence the essence of any species possesses something over and above its genus. But existence itself, *ipsum esse*, which is God's essence, does not comprise within itself any factor that is added to some other factor. Accordingly God is not a species of any genus.Compendium of Theology, pp. 17–18
What a thing is, but not that it is, comes from its genus... But that which God is, is very existence itself. Therefore He cannot be a genus. Moreover, every genus is divided by some differences. But no differences can be apprehended in very existence itself... there cannot be any difference that does not share in existence, since non-being is not the specific difference of anything.Compendium of Theology, pp. 17–18