To begin, one must understand what both poetry and prose are.
Poetry, according to Merriam-Webster, is a
writing that formulates a concentrated imaginative awareness of experience in language chosen and arranged to create a specific emotional response through meaning, sound, and rhythm.
Prose, on the other hand, is
a literary medium distinguished from poetry especially by its greater irregularity and variety of rhythm and its closer correspondence to the patterns of everyday speech.
That being said, poetry and prose are distinguished from each other based solely upon the rhythm of which each are read. In regards to the titles of poems, the title's significance is irrelevant in regards to the piece being a poem or a prose. The title of a work is the title of a work. The significance of the title of a work is important regardless of the rhythm of a text. One cannot disregard the significance of a text based only upon the rhythm, or lack of rhythm, established in the piece.
Outside of that, the title of any work is very important. Many times, in regards to a poem, novel, novella, or short story, the title of the piece makes the reader think about how the title relates to the piece.
The difference about the importance of a poem's title lies in the fact that the title sometimes allows the reader to come to a different understanding of the poem's meaning. If one is to disregard the title of a poem, the reader can miss the true meaning behind the poem.
For example, read the following poem (the title has been removed):
In the grey evening
I see a long green serpent
With its tail in the dahlias
It lies In loops across the grass
And drinks softly at the faucet.
I can hear it swallow.
Based upon the descriptions provided in the poem, a reader would think that the poem is about a snake. Instead, the poem is titled "The Garden Hose" and was written by Beatrice Janosco.
Therefore, the title of a poem is very important given the object described would have been lost without the title signalling to the reader what the poet is actually describing.