The connotation (suggestions and associations) of words is at the center of what poets do. Words are what poets arrange and manipulate to create poems, so what those words mean--connotatively as well as denotatively (the literal, dictionary definition)--is an essential element of poetry.
Let's look at an example of a Robert Frost poem, "Dust of Snow":
The way a crow
Shook down on me
The dust of snow
From a hemlock tree
Has given my heart
A change of mood
And saved some part
Of a day I had rued.
The poem establishes contrasts, in part with connotations. Crows are usually associated with death. They are scavengers and dark black like the night and Poe uses one exactly in this way in a famous poem. Crows represent death. When Frost uses a crow he is drawing on these associations. Yet the crow's act of shaking a tree limb and dumping snow on the speaker raises the speaker's mood, saving a day he had been dreading.
"Hemlock" is, of course, associated with poison. The poem, therefore, features a bird representing death in a tree representing poison, shaking snow on the speaker in stanza one, which leads to the speaker's change of mood, for the better, in stanza two.
Stanza one contrasts with stanza two. The stanzas exhibit a cause-effect relationship, as well as an external-internal relationship. The external causes an internal change for the better.
A crow is literally just a bird. A hemlock tree is literally just another tree. Yet, in the poem, connotatively, out of death arises a lighter mood, a "saved" day. Nothing earth shattering, just a subtle, playful change of mood. Or, if that seems a stretch to you, at the least the usually foreboding crow acts playfully, jokingly; demonstrates a sense of humor. Either way, the contrasts are established by the connotations.
Poets play with words and their connotations. At least Frost does here.