Proportion between different realities allowing them to be qualified by one another, or by a single term that applies to all because of a certain similarity. In a certain sense, analogy stands midway between the cataphatic and apophatic approaches (see those entries).
It is in St. Thomas Aquinas that we find the classical theory of analogy, which makes it possible to speak about God without compromising His transcendence or incomprehensibility. Thus, the terms we apply both to God and to creatures are used by analogy of proportionality: to say “God is good,” for example, does not mean the same thing as saying “this person is good.” The goodness of God is to God as human goodness is to man, yet in an infinitely higher and more perfect mode.
Analogy is linked to being itself: God is Being by essence, whereas creatures possess being only in a participative and derivative manner. It reveals both distance and proximity, separation and communion. Between God and the world there is neither pure identity (which would be pantheism) nor absolute otherness (which would be dualism), but a proportional similarity that grounds every possibility of theological knowledge and language. Analogy thus expresses the ontological bond between the Created and the Uncreated; it is the very structure of participation, through which finite things point toward the Infinite from which they proceed.
From this point of view, to know, to love, or to name God is always to participate in His Being in an analogical mode: the intellect ascends toward its principle by recognizing in every created perfection a reflection of the Perfect. Analogy thus becomes the very language of metaphysics — a discourse that unites without confusion and distinguishes without division.
For further reading: Thomas Aquinas, Summa Theologiae I, q. 13; Jean Borella, The Crisis of Religious Symbolism, II; Bruno Bérard, Metaphysics for Everyone (Angelico Press) — English edition of Métaphysique pour tous (Paris, L’Harmattan, 2021); also translated into Italian Sui sentieri della metafisica, Spanish ¿Qué es la metafísica?, and German Was ist Metaphysik?