“A poem is a program that executes in the brain of the reader.” – Richard P. Gabriel 
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The text of the poem interacts with the mental residue of a reader’s lifetime of experience. That interaction produces a meaning or interpretation that will differ in at least some small way from every other reader’s. (See Personal Context for an example.)
Meaning is not put *into* the poem, or into any text; it is constructed by the receiver’s brain in response to clues delivered as words (Conduit Metaphor). We communicate successfully because we share experiences in common and because we’re trained from an early age in how to interpret words and sentences so that our meanings are close enough to other people’s for our life’s purposes.