There are two maxims in Lucretius that suffice, even to this day, to distinguish a thinker who is a naturalist from one who is not. "Nothing," he says, "arises in the body in order that we may use it, but what arises brings forth its use." This is that discarding of final causes on which all progress in science depends. The other maxim runs: "One thing will grow plain when compared with another: and blind night shall not obliterate the path for thee, before thou hast thoroughly scanned the ultimate things of nature; so much will things throw light on things." Nature is her own standard; and if she seems to us unnatural, there is no hope for our minds.
He later goes on to add more to his account of naturalism, discussing its role in Lucretius's poetry:
No, the poetry of nature may be discerned merely by the power of intuition which it awakens and the understanding which it employs. These faculties, more, I should say, than our moodiness or stuffy dreams, draw taut the strings of the soul, and bring out her full vitality and music. Naturalism is a philosophy of observation, and of an imagination that extends the observable; all the sights and sounds of nature enter into it, and lend it their directness, pungency, and coercive stress. At the same time, naturalism is an intellectual philosophy; it divines substance behind appearance, continuity behind change, law behind fortune. It therefore attaches all those sights and sounds to a hidden background that connects and explains them. So understood, nature has depth as well as surface, force and necessity as well as sensuous variety. Before the sublimity of this insight, all forms of the pathetic fallacy seem cheap and artificial. Mythology, that to a childish mind is the only possible poetry, sounds like bad rhetoric in comparison. The naturalistic poet abandons fairy land, because he has discovered nature, history, the actual passions of man. His imagination has reached maturity; its pleasure is to dominate, not to play.
That last note sounds rather more ominous in our day and age than it could have in Santayana's; but it's in a long tradition of what counts as maturity of mind.
The book itself is quite interesting; it's intended to be a "first broad lesson in the history of philosophy -- and, perhaps, in philosophy itself," but it does so by looking at Lucretius, Dante, and Goethe as each summing up an entire philosophical approach to the world: Lucretius is the poet of naturalism, Dante the poet of supernaturalism, Goethe the poet of romanticism. While poetry doesn't allow room for the heavy step-by-step reasoning of philosophical investigation, Santayana thinks it has a great affinity for the visions of the world that such investigation eventually reaches. Thus, what he is trying to do in the second passage above is give an indication of how naturalism allows for the sublimity that makes a Lucretius, i.e., a truly great poet writing a truly great naturalistic poem, possible in the first place.
If I read him correctly, Santayana doesn't think Lucretian naturalism is quite adequate. The other two poets Santayana considers are Dante and Goethe, who with Lucretius he takes to sum up all of European philosophy, and I think his sympathies are more on the Goethe side of things -- Goethe is, so to speak, the synthesis of the thesis of Lucretius and the antithesis of Dante, and is the poet who sums up the modern age. But in the end Santayana faces us with the puzzle that each of the three gives us something that is very desirable, both rationally and vitally: philosophy and poetry alike find in each of naturalism, supernaturalism, and romanticism something they cannot afford to lose. Thus in the end I think Santayana is committed to saying that, sitting at the feet of Lucretius, Dante, and Goethe we learn that we still have much to learn, for the philosophical has not yet been finished, and the poet has not yet arisen, that can give us the vision of the world that captures everything that reason and life need and find in each of the three poets.