"Eating poetry" is an odd image that we usually do not relate to reading a poem. It conjures a vision of tearing a page of poetry from a book, chewing it up, and swallowing it. Strand's speaker uses this as a metaphor for not just running our eyes over the words of a poem but internalizing what the poet is saying and feeling. Just as we feel different inside when we eat food, so we should feel bodily different, the speaker suggests, when we truly internalize a poem's message.
Poetry is more than just an intellectual exercise, Strand asserts. It encompasses a reality larger than simply understanding the words on a page. We need to feel it. At best, it changes us: "I am a new man," the speaker says.
Strand has his speaker contrast himself to the librarian. She is the guardian of the words in the library but also distanced from them. Strand's speaker is likened, however, to a dog who has with great enthusiasm swallowed the words of a poem. His enthusiasm and gusto are alarming and alienating to the librarian. As the speaker says,
She does not understand.
When I get on my knees and lick her hand,
Reading poetry is the same as eating poetry, when we feel the emotions a poem is trying to evoke and are transformed by them in addition to merely understanding the words.