The effect of an apostrophe in poetry is to personify or bring to life something not living, so the poet is able to address it directly. This puts the subject in a form to which the reader relates.
Using the apostrophe in poetry helps to emphasize what the poet is saying and gives his words greater power. In his poem "Death Be Not Proud," John Donne uses the apostrophe to personify death and, in so doing, take away some of its mystery. When he confronts death as if it were a person, he wields more power over it and is able to tell it "nor yet canst thou kill me."
The type of apostrophe used in poetry has nothing to do with the punctuation mark by the same name.