Lines 7-14 Summary

Get out the microscope, because we’re going through this poem line-by-line.

the idolatry of the self and the desecration of the self and the dissipation of the self;

Not to be rude, but poets can be really egocentric. Don't worry, though. Paz is onto them! This line compares poetry idolatry, desecration, and dissipation of the self. All those ands are another example of our old pal polysendeton—using conjunctions (like "and" or "but") repeatedly in the same sentence. Also, the repetition of "of the self" at the end of each phrase is a technique known as epistrophe.
So why all this repetition of selfhood? Well, because poetry is basically a self-absorbed art. The poet usually writes it alone, and the reader usually reads it alone. So it is, in a way, a self-glorifying art: the poet puts his whole self into the art.
But then it's also the "desecration" of the self. This means using something sacred for a profane use. So the poem implies that the self is sacred (maybe that's why it's idolatrized right before it's desecrated), but that poetry brings it down to the nitty gritty, the real world.
Finally, poetry is the dissipation of the self, or the dissolving or vanishing of the self. Maybe because the poet puts himself into poetry, he loses himself, and disappears a little bit.
This is all to say that poetry is very self-absorbed.

the beheading of epithets, the burial of mirrors;

Here the poem compares poetry to cutting off epithets' heads (we didn't even know epithets had heads…) and burying mirrors. This is all a really indirect way of saying that poetry doesn't say things directly.
Epithets are adjectives that go along with someone's name that tells you something intrinsic to their character, like Richard the Lion-Hearted or Charles the Bald. This line personifies the epithet, only to chop off its head (Epithet the Beheaded?), which means that poetry doesn't just name something for what it is. It uses metaphors or similes or all kinds of other figures to get its point across.
It's the same thing with burying mirrors. Poetry doesn't just hold up an identical image of what it's describing. It adds other images and symbols to make us see whatever is being described not exactly as it is, like in a Realistic novel, but in a different light.
In fact, these lines do just that. They don't just say, "Poetry is a literary form that often employs rhyme and meter." Instead, they tell you that poetry is beheading epithets and burying mirrors. Clever how the form and the content work together there, eh?

the recollection of pronouns freshly cut in the garden of Epicurus, and the garden of Netzahualcoyotl;

Woah. Now we get some history lessons. Apparently, poetry is like something you can get out of a couple of famous gardens, Epicurus' and Netzahualcoyotl's. So who are those guys? Well, let us tell you:
Epicurus was an ancient Greek philosopher who had a philosophy school called the Garden, and Netzahualcoyotl was the poet-king of the pre-Hispanic city-state Texcoco. His verses about flowers and plants are so famous that Mexican schoolchildren memorize them to this day. (See "Shout-Outs" for more information.)
So both of these philosophers used gardens as a metaphor, either in their teaching or their poetry, and Paz is following in their footsteps. He also makes a metaphor that compares that measly part of speech the pronoun to flowers that would be cut from a garden. Here words are something organic that grows with the help of a gardener, or a poet.

the flute solo on the terrace of memory and the dance of flames in the cave of thought;

We're still comparing poetry to things, and this time it's a shadow puppet show! Poetry is like the memory of a flute's song, or the flickering fire in a cave.
Poetry is compared to other arts here, particularly music, as though the poet were writing down a piece of music he once heard.
The philosophy theme stays strong, too, as the cave of thought is probably a reference to Plato's Cave, from The Republic (more on this in the "Shout-Outs" section). Poetry once again works as something that comes between us and the real world, softening it with metaphors but never being direct.

the migrations of millions of verbs, wings and claws, seeds and hands;
the nouns, bony and full of roots, planted on the waves of language;

And now poetry is taking over the world, like killer bees or fire ants. Head for the hills! It's compared to mass migrations of what could be birds or even people.
The millions of verbs in this line, which make up the poetry migration, are first compared to birds in a metaphor (what else has wings and claws?), then to what is probably human beings, because of the hands.
The visual image is pretty wild, and makes you think of a huge flock of birds flying south for the winter. The idea is that poetry is alive and part of the world, and that it is in motion. Even though it's just dry ink on a dry page, the images bring it to life.
So verbs are on the move, migrating like birds, and the nouns are plants, staying put. It makes sense, right? Verbs = actions, nouns = things. The nouns' vegetable nature doesn't make them any less alive than the verbs though: they're rooted in language.

the love unseen and the love unheard and the love unsaid: the love in love.

And, you saw this coming, right? Poetry is L-O-V-E. Except that it's not your everyday, run-of-the-mill love. No! Poetry is for those guys who are too afraid to express their love, so it ends up being the love that isn't—isn't seen, isn't heard, and isn't said. It's written.
The repetition of the words "the love" at the beginning of these four phrases is an example of anaphora and, you guessed it, all those "and"s demonstrate more use of our friend polysendeton. It kind of makes the sentence flow, like the poetic speaker is just high on love and can't stop going on and on and on about it. (See what we did there?)

Syllables seeds.

The poem's final line is a little bit mysterious, a sentence with no verb, more just a statement or definition: "Syllables seeds." This wraps up the whole organic, vegetation metaphor really nicely, as though the meaningless parts of words were the seeds from which the poet sows his garden.
There are a couple of interesting poetic devices going on here. First of all, the repeated S sound is an example of alliteration that brings the poem to a close on a nice, wizard-like whisper. Secondly, this line is in italics, which sets it off from the rest of the poem as though it were indeed some sort of magic spell.