The statement that God is simple refers to the nature of his being—that is, that he is not composed of parts. Because he has no parts, he has no extension in space or time. He is a purely spiritual being. His attributes are equivalent to his essence. We say that God is love. We can also say that God is mercy; God is justice; God is omniscience, with respect to every attribute of God.
The human soul is also a spiritual substance, not composed of parts. That is why it survives separation from the body at death. Yet we refer to two distinct faculties of the soul: intellect and will. Using these faculties of our soul, we are able to know and to love, to intellectually apprehend reality, and to make choices.
Let’s make an analogy with God. A human being, using his intellect, can know himself.
He can never know himself perfectly, though. He can’t know the state of every atom, every molecule, in his body, at any instant. He can’t apprehend the complexity of his psychological makeup perfectly. So his knowledge of himself is imperfect.
God’s knowledge, however, is perfect and complete. God knows all things, including himself. God’s knowledge of himself is perfect and complete. You might, with analogy to human knowledge, say that from all eternity, God forms a perfect idea of himself.
God’s idea of himself is so perfect that there is nothing lacking in his idea of himself. Everything in the subject is present in the idea—including the aspect of personhood. From all eternity, God (whom we can now call the Father) generates a perfect idea of himself, perfectly including every aspect, including personhood. We call this the Word, or Son.
Both Father and Son totally possess the one divine nature, which, being simple, can not be divided. But each is a Person.
The human soul can both know and love. So can God. The Father and Son love each other, generating a love so perfect that it also does not lack the aspect of personhood. This is the Holy Spirit.
Through the divine intellect, the Son is eternally generated. Through the divine will or the movement of divine love, the Holy Spirit is eternally generated. And the substance of the divine nature remains one being, expressed as three Persons.