The title is pretty straightforward: "Archaic Torso of Apollo" describes—you got it—an archaic (old) torso of Apollo. However, if we investigate it a bit more closely, we see that it's actually very valuable. First of all, nothing in the poem actually tells us what the speaker's describing. We can tell it's a statue when he finally mentions that it's "stone" in line 9, but until then, it seems a bit mysterious. Is it a real person? Is it an animal? The title clears all of this up.
It also adds more layers to the experience described in the poem. Knowing that it's an ancient, or "archaic," work of art gives it a sense of historicity and depth. The fact that it's just a "torso" explains to us why "we cannot know his legendary head," since the fragment of a statue doesn't have one. Finally, knowing that it's Apollo—god of light, music, and poetry—sets us up to be a little in awe of this figure, as well as in an artistic mindset, before we even start.
Labeling this inanimate "character" Apollo draws upon a whole tradition of the Apollonian mode (that is, a mode that follows in Apollo's footsteps) in art. This philosophical and artistic concept, developed by Nietzsche, draws upon the values inspired by Apollo, the giver of light—illumination, of art (in this case, both poetry and sculpture). However, the polar opposite, the Dionysian mode (embodied by the Greek god of wine, Dionysus) is also summoned up here in the sexualized "dark center where procreation flared" (8) and the "wild beast's fur" (12). As a result, the statue exudes both pure spiritual radiance and hints of sensual pleasure, pointing readers to both sides of human nature.
Whew, that seems like a lot to get from the title. Maybe we're reading into it a bit much—but don't blame us; Rilke made us do it.