One difference between a poem's meaning and its purpose is found in John Donne's "The Flea," where the author, who specialized in metaphysical poetry, nevertheless has a very physical goal. A flea sucks the blood of both the poet and his lover; thus "three lives in one flea" become a "marriage bed." When the lover kills the flea, its life is "so much honour ... when thou yield'st to me." Donne's poem achieves meaning in exploring the link between nature and the lovers. Donne's purpose behind the poem is to bed the woman.
A poet's meaning may therefore come from purer motives than his purpose, as is often the case with Shakespeare, whose "Sonnet 18" begins with "Shall I compare thee to a summer's day?" He goes on to contrast the day and his lover's qualities, ending with the promise "this [the poem] gives life to thee." Shakespeare's sonnet, however, tells us nothing whatsoever about the woman, not even her name. The poem's stated meaning is to glorify the woman; Shakespeare's real purpose is to glorify his own verse.
e.e. cummings' "Buffalo Bill" is a satirical work calling the killer of buffalo "defunct" and a "blue-eyed boy," a favorite of "Mister Death." The poem's meaning is to deflate the Western legend and remind people that Buffalo Bill practiced genocide, since Indians died with those buffalo. However, cummings shapes his poem as an arrow, with "Buffalo Bill," "Jesus" and "Mister Death" at its three points. His purpose therefore is to glorify our icons, even the flawed human ones.
No poet has greater variance between meaning and purpose than Emily Dickinson. Most of her poetry seems composed in emotional turmoil and gives us phrases such as one in "Poem 1260:" "You who were Existence yourself forgot to live." Her purpose is to express anger at a mentor; her poem's meaning encompasses deeper existential ideas. No one can read that phrase without a cringe; its purpose was temporal, but the meaning is immortal.